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All Textbook Solutions for Trigonometry (MindTap Course List)

59PS Find if is between 0 and 90. Round your answers to the nearest tenth of a degree. tan=6.2703 Find if is between 0 and 90. Round your answers to the nearest tenth of a degree. sec=1.0191 Find if is between 0 and 90. Round your answers to the nearest tenth of a degree. sec=8.0101 Find if is between 0 and 90. Round your answers to the nearest tenth of a degree. csc=1.8214 Find if is between 0 and 90. Round your answers to the nearest tenth of a degree. csc=4.2319 65PS Find if is between 0 and 90. Round your answers to the nearest tenth of a degree. cot=7.0234 Use a calculator to find a value of between 0 and 90 that satisfies each statement. Write your answer in degrees and minutes rounded to the nearest minute. cos=0.4112 Use a calculator to find a value of between 0 and 90 that satisfies each statement. Write your answer in degrees and minutes rounded to the nearest minute. sin=0.9459 Use a calculator to find a value of between 0 and 90 that satisfies each statement. Write your answer in degrees and minutes rounded to the nearest minute. cot=5.5764 70PS 71PS 72PS To further justify the Cofunction. Theorem use your calculator to find a value for the given pair of trigonometric functions. In each case, the trigonometric functions arc cofunctions of one another, and the angles arc complementary angk i Round your answers to four places past the decimal point. sin23,cos67 74PS To further justify the Cofunction. Theorem, use your calculator to find a value for the given pair of trigonometric functions. In each case, the trigonometric functions arc cofunctions of one another, and the angles arc complementary angki Round your answers to four places past the decimal point. sec34.5,csc55.5 To further justify the Cofunction. Theorem, use your calculator to find a value for the given pair of trigonometric functions. In each case, the trigonometric functions arc cofunctions of one another, and the angles arc complementary angles. Round your answers to four places past the decimal point. sec6.7,csc83.3 77PS 78PS 79PS 80PS What happens when you try to find A for sin A = 1.234 on your calculator? Why does it happen?What happens when you try to find B for sin B = 4.321 on your calculator? Why does this happen?What happens when you try to find tan 90 on your calculator? Why does this happen?What happens when you try to find cot 0 on your calculator? Why does this happen?85PS 86PS 87PS Sundials The Moorish sundial is designed so that the shadow of the gnomon (the vertical triangular piece) is consistent at each hour from one day to the next. This allows the hours to be marked on the sundial using a single scale that is not affected by the changes in the Suns path during the year. If the sundial is positioned so that the gnomon is aligned along a longitudinal line from north to south, then at exactly noon the gnomon will cast a shadow due north. Figure 7 As the sun moves, the shadow will sweep out an angle toward the east, labeled in Figure 7, called the shadow angle. This angle can be calculated using the formula tan=sintan(h15) where is the latitude of the position of the sundial and h is a number of hours from noon. The latitude of Goose Pimple Junction,w Virginia, is 36.597. Find the shadow angle for a sundial in this town at 5:00 p.m. Round to the nearest tenth of a degree.89PS 90PS 91PS Find sin,cos, and tan for each value of . (Do not use calculators.) 135 Find the remaining trigonometric functions of based on the given information. cos=5/13 and terminates in QIII Find the remaining trigonometric functions of based on the given information. tan=3/4and terminates in QII 95PS 96PS 97PS 98PS 99PS Given cot=x for some value x. Which of the following correctly shows how to use a calculator to approximate ? a. tan1(1/x) b. 1/tan1(x) c. cos(x)/sin(x) d. cos1(x)/sin1(x)For Questions 1 through 4, fill in each blank with the appropriate word. To count the number of significant digits in a number, count all the digits from _________ to _________ beginning with the _________ _________ digit on the left. If no decimal point is present, trailing zeros are_________ counted.For Questions 1 through 4, fill in each blank with the appropriate word. If the sides of a triangle are accurate to three significant digits, then angles should be measured to the nearest _________ of a degree, or the nearest _________ minutes.For Questions 1 through 4, fill in each blank with the appropriate word. To solve a right triangle means to find all of the missing _________ and _________.4PS 5PS For Problems 5 through 8, determine the number of significant digits in each value. a. 374 b. 0.0374 c. 3.7400 d. 374.000 7PS 8PS Problems 9 through 22 refer to right triangle ABC with C=90. Begin each problem by drawing a picture of the triangle with both the given and asked-for information labeled appropriately. Also, write your answers for angles in decimal degrees. If A=42 and c=89 cm, find b.10PS 11PS Problems 9 through 22 refer to right triangle ABC with C=90. Begin each problem by drawing a picture of the triangle with both the given and asked-for information labeled appropriately. Also, write your answers for angles in decimal degrees. If A =64 and h = 55 m, find c.13PS Problems 9 through 22 refer to right triangle ABC with C=90. Begin each problem by drawing a picture of the triangle with both the given and asked-for information labeled appropriately. Also, write your answers for angles in decimal degrees. If B=24.5 and c = 3.45 ft, find a.Problems 9 through 22 refer to right triangle ABC with C=90. Begin each problem by drawing a picture of the triangle with both the given and asked-for information labeled appropriately. Also, write your answers for angles in decimal degrees. If B=55.33 and b = 12.34 yd, find a.16PS 17PS Problems 9 through 22 refer to right triangle ABC with C=90. Begin each problem by drawing a picture of the triangle with both the given and asked-for information labeled appropriately. Also, write your answers for angles in decimal degrees. If a = l6 cm and b = 29 cm, find A.19PS 20PS Problems 9 through 22 refer to right triangle ABC with C=90. Begin each problem by drawing a picture of the triangle with both the given and asked-for information labeled appropriately. Also, write your answers for angles in decimal degrees. If c = 45.54 ft and a = 23.32 ft. find B.22PS Problems 23 through 38 refer to right triangle ABC with C=90. In each case, solve for all the missing parts using the given information. (In Problems 35 through 38, write your angles in decimal degrees.) A=25,c=24m Problems 23 through 38 refer to right triangle ABC with C=90. In each case, solve for all the missing parts using the given information. (In Problems 35 through 38, write your angles in decimal degrees.) A=71,c=36m 25PS 26PS Problems 23 through 38 refer to right triangle ABC with C=90. In each case, solve for all the missing parts using the given information. (In Problems 35 through 38, write your angles in decimal degrees.) A=1042,b=5.932cm 28PS Problems 23 through 38 refer to right triangle ABC with C=90. In each case, solve for all the missing parts using the given information. (In Problems 35 through 38, write your angles in decimal degrees.) B=76,c=5.8ft Problems 23 through 38 refer to right triangle ABC with C=90. In each case, solve for all the missing parts using the given information. (In Problems 35 through 38, write your angles in decimal degrees.) B=21,c=4.2ft Problems 23 through 38 refer to right triangle ABC with C=90. In each case, solve for all the missing parts using the given information. (In Problems 35 through 38, write your angles in decimal degrees.) B=2630,b=324mm Problems 23 through 38 refer to right triangle ABC with C=90. In each case, solve for all the missing parts using the given information. (In Problems 35 through 38, write your angles in decimal degrees.) B=5330,b=125mm 33PS 34PS Problems 23 through 38 refer to right triangle ABC with C=90. In each case, solve for all the missing parts using the given information. (In Problems 35 through 38, write your angles in decimal degrees.) a=37ft,b=87ft Problems 23 through 38 refer to right triangle ABC with C=90. In each case, solve for all the missing parts using the given information. (In Problems 35 through 38, write your angles in decimal degrees.) a=99ft,b=85ft Problems 23 through 38 refer to right triangle ABC with C=90. In each case, solve for all the missing parts using the given information. (In Problems 35 through 38, write your angles in decimal degrees.) b=377.3inches,c=588.5inches Problems 23 through 38 refer to right triangle ABC with C=90. In each case, solve for all the missing parts using the given information. (In Problems 35 through 38, write your angles in decimal degrees.) a = 62.3cm, c = 73.6 cm In Problems 39 and 40, use the information given in the diagram to find A to the nearest degree.In Problems 39 and 40, use the information given in the diagram to find A to the nearest degree.41PS 42PS 43PS 44PS 45PS Figure 8 shows two right triangles drawn at 900 to each other. For Problems 45 through 48, redraw Figure 8, label it as the problem indicates, and then solve the problem. Figure 8 If ABD=53, C = 48, and BC = 24, find x and then find h.Figure 8 shows two right triangles drawn at 900 to each other. For Problems 45 through 48, redraw Figure 8, label it as the problem indicates, and then solve the problem. Figure 8 If AC = 32. h = 19, and C = 41, find ABD .Figure 8 shows two right triangles drawn at 900 to each other. For Problems 45 through 48, redraw Figure 8, label it as the problem indicates, and then solve the problem. Figure 8 If AC = 19, h = 32, and C = 49, find ABD .49PS 50PS 51PS 52PS In Figure 9, the distance from A to D is y, the distance from D to C is x. and the distance from C to B is h. Use Figure 9 to solve Problems 49 through 54. Figure 9 A=32,BDC=57, and y = 11, find x.In Figure 9, the distance from A to D is y, the distance from D to C is x. and the distance from C to B is Ii. Use Figure 9 to solve Problems 49 through 54. Figure 9 A=32,BDC=61, and y=14, find x.Suppose each edge of the cube shown in Figure 10 is 5.00 inches long. Find the measure of the angle formed by diagonals CF and CH. Round your answer to the nearest tenth of a degree. Figure 10 Suppose each edge of the cube shown in Figure 10 is 3.00 inches long. Find the measure of the angle formed by diagonals DE and DG. Round your answer to the nearest tenth of a degree. Figure 10 Suppose each edge of the cube shown in Figure 10 is x inches long. Find the measure of the angle formed by diagonals CF and CH. Round your answer to the nearest tenth of a degree. Figure 10 Soccer A regulation soccer field has a rectangular penalty area that measures 132 feet by 54 feet. The goal is 24 feet wide and centered along the back of the penalty area. Assume the goalkeeper can block a shot 6 feet to either side of his or her position for a total coverage of 12 feet. (Source: FĂ©dĂ©ration Internationale de Football Association) A penalty kick is taken from a corner of the penalty area at position A (see Figure 11). The goalkeeper stands 6 feet from the goalpost nearest the shooter and can thus block a shot anywhere between the middle of the goal and the nearest goalpost (segment CD). To score, the shooter must kick the ball within the angle CAE. Find the measure of this angle to the nearest tenth of a degree. Figure 11 59PS Soccer A regulation soccer field has a rectangular penalty area that measures 132 feet by 54 feet. The goal is 24 feet wide and centered along the back of the penalty area. Assume the goalkeeper can block a shot 6 feet to either side of his or her position for a total coverage of 12 feet. (Source: FĂ©dĂ©ration Internationale de Football Association) A penalty kick is taken from the center of the penalty area at position A (see Figure 13). The goalkeeper stands in the center of the goal and can thus block a shot anywhere along segment CD. To score, the shooter must kick the ball within the angle CAE or angle DAF. Find the sum of these two angles to the nearest tenth of a degree. Figure 13 61PS 62PS 63PS 64PS Ferris Wheel In 1897, a Ferris wheel was built in Vienna that still stands today. It is named the Riesenrad, which translates to the Great Wheel. The diameter of the Riescnrad is 197 feet. The top of the wheel stands 209 feet above the ground. Figure 14 is a model of the Riesenrad with angle 0 the central angle that is formed as a rider moves from the initial position P0 to position P1. The rider is h feet above the ground at position P1. a. Find h if is 120.0. b. Find h is is 2l0.0. c. Find h if is 3l5.0. Figure 14 Ferris Wheel A Ferris wheel with a diameter of 165 feet was built in St. Louis in 1986. It is called Colossus. The top of the wheel stands 174 feet above the ground. Use the diagram in Figure 14 as a model of Colossus. a. Find h if is 150.0. b. Find h 11 is 240.0. c. Find h if is 315.0.Observation Wheel the London Eye has a diameter of 135 meters. A rider boards the London Eye at ground level. Through what angle has the wheel rotated when the rider is 445 meters above ground for the first time?Observation Wheel The High Roller, located on the Las Vegas Strip in Paradise. Nevada, is currently the largest observation wheel in the world with a diameter of 520 feet. The top of the wheel stands 550 feet above the ground. Find the height of a rider after the wheel has rotated through an angle of 110. Assume the rider boards at the bottom of the wheel.Human Cannonball In Example 2 of Section 1.2, we found the equation of the path of the human cannonball. At a Washington County Fair in Oregon. David Smith. Jr., The Bullet, was shot from a cannon. As a human cannonball, he reached a height of 70 feet before landing in a net 160 feet from the cannon. In that example we found the equation that describes his path is y=7640(x80)2+70 for 0x160 Graph this equation using the window 0x180, scale = 20; 0 0y80, scale = 10 Then zoom in on the curve near the origin until the graph has the appearance of a straight line. Use ITRACEI to find the coordinates of any point on the graph. This point defines an approximate right triangle (Figure 15). Use the triangle to find the angle between the cannon and the horizontal. Figure 15 70PS 71PS 72PS 73PS 74PS Find the remaining trigonometric ratios for based on the given information. sin=32 with in QII Find the remaining trigonometric ratios for based on the given information. Cos=15 with in QIV Find the remaining trigonometric ratios for based on the given information. sec=2 with in QIII Find the remaining trigonometric ratios for based on the given information. csc=2 with in QIII 79PS 80PS 81PS A Ferris wheel has a radius of 45 feet and the bottom of the wheel stands 6.5 feet above the ground. Find the height of a rider if the wheel has rotated 1400 after the rider was seated. a. 64 feet b. 95 feet c. 86 feet d. 80 feet For Questions 1 through 4, fill in each blank with the appropriate word. An angle measured upward from a horizontal line is called an angle of _____ and an angle measured downward from a horizontal line is called an angle of ____________.For Questions 1 through 4, fill in each blank with the appropriate word. If an observer positioned at the vertex of an angle views an object in the direction of the nonhorizontal side of the angle, then this side is called the ______ ___ ______ of the observer.3PS 4PS 5PS 6PS 7PS 8PS 9PS 10PS 11PS 12PS Solve each of the following problems. In each case, be sure to make a diagram of the situation with all the given information labeled. Geometry the two equal sides of an isosceles triangle are each 42 centimeters. If the base measures 32 centimeters, find the height and the measure of the two equal angles.Solve each of the following problems. In each case, be sure to make a diagram of the situation with all the given information labeled. Geometry An equilateral triangle (one with all sides the same length) has an altitude of 12.3 inches. Find the length of the side&Solve each of the following problems. In each case, be sure to make a diagram of the situation with all the given information labeled. Geometry The height of a right circular cone is 25.3 centimeter. If the diameter of the base is 10.4 centimeters, what angle does the side of the cone make with the base (Figure 13)? Figure 13 Solve each of the following problems. In each case, be sure to make a diagram of the situation with all the given information labeled. Geometry The diagonal of a rectangle is 348 millimeters, while the longer side is 278 millimeters. Find the shorter side of the rectangle and the angles the diagonal makes with the sides.Solve each of the following problems. In each case, be sure to make a diagram of the situation with all the given information labeled. Length of an Escalator How long should an escalator be jilt is to make an angle of 33 with the floor and carry people a vertical distance of 21 feet between floors?Solve each of the following problems. In each case, be sure to make a diagram of the situation with all the given information labeled. Height of a Hill A road up a hill makes an angle of 6.5 with the horizontal. If the road from the bottom of the hill to the top of the hill is 2.5 miles long, how high is the hill?Solve each of the following problems. In each case, be sure to make a diagram of the situation with all the given information labeled. Length of a Rope A 72.5-foot rope from the top of a circus tent pole is anchored to the ground 43.2 feet from the bottom of the pole. What angle does the rope make with the pole? (Assume the pole is perpendicular to the ground.)20PS Solve each of the following problems. In each case, be sure to make a diagram of the situation with all the given information labeled. Angle of Elevation If a 73.0-foot flagpole casts a shadow 51.0 feet long, what is the angle of elevation of the sun (to the nearest tenth of a degree)?Solve each of the following problems. In each case, be sure to make a diagram of the situation with all the given information labeled. Angle of Elevation If the angle of elevation of the sun is 7340 when a building casts a shadow of 37.5 feet, what is the height of the building?Solve each of the following problems. In each case, be sure to make a diagram of the situation with all the given information labeled. Angle of Depression A person standing 150 centimeters from a mirror notices that the angle of depression from his eyes to the bottom of the mirror is 12, while the angle of elevation to the top of the mirror is 11. Find the vertical dimension of the mirror (Figure 14). Figure 14 Solve each of the following problems. In each case, be sure to make a diagram of the situation with all the given information labeled. Width of a Sand Pile A person standing on top of a 15-foot high sand pile wishes to estimate the width of the pile. He visually locates two rocks on the ground below at the base of the sand pile. The rocks are on opposite sides of the sand pile, and he and the two rocks are in the same vertical plane. If the angles of depression from the top of the sand pile to each of the rocks are 290 and 17. how far apart are the rocks?Figure 15 shows the topographic map e used in Example 4 of this section. Recall that Stacey is at position S and Amy is at position A. In Figure 15, Travis, a third hiker, is at position T. Topographic Map Reading If the distance between A and Ton the map in Figure 15 is 0.50 inch, find each of the following: a. the horizontal distance between Amy and Travis b. the difference in elevation between Amy and Travis c. the angle of elevation from Travis to Amy Figure 15 Figure 15 shows the topographic map e used in Example 4 of this section. Recall that Stacey is at position S and Amy is at position A. In Figure 15. Travis. a third hiker, is at position T. Topographic Map Reading If the distance between S and T on the map in Figure 15 is 58 inch, find each of the following: a. the horizontal distance between Stacey and Travis b. the difference in elevation between Stacey and Travis c. the angle of elevation from Travis to Stacey Figure 5 Distance and Bearing Problems 27 through 32 involve directions in the form of bearing, which we defined in this section. Remember that bearing is always measured from a north-south line. Lompoc, California, is 18 miles due south of Nipomo. Buellton, California, is due cast of Lompoc and S 65 E from Nipomo, how far is Lompoc from Buellton?Distance and Bearing Problems 27 through 32 involve directions in the form of bearing, which we defined in this section. Remember that bearing is always measured from a north-south line. A tree on one side of a river is due west of a rock on the other side of the river. From a stake 21.0 yards north of the rock, the bearing of the tree is S 18.2 W. How far is it from the rock to the tree?Distance and Bearing Problems 27 through 32 involve directions in the form of bearing, which we defined in this section. Remember that bearing is always measured from a north-south line. A boat leaves the harbor entrance and travels 25 miles in the direction N 420 E. The captain then turns the boat 90 and travels another 18 miles in the direction S 48 E. At that time, how far is the boat from the harbor entrance, and what is the bearing of the boat from the harbor entrance (Figure 16)? Figure 16 Distance and Bearing Problems 27 through 32 involve directions in the form of bearing, which we defined in this section. Remember that bearing is always measured from a north-south line. A man wandering in the desert walks 2.3 miles in the direction S 310 W. He then turns 90 and walks 3.5 miles in the direction N 59 W. At that time, how far is he from his starting point, and what is his bearing from his starting point?31PS 32PS Height of a Door From a point on the floor the angle of elevation to the top of a door is 47, while the angle of elevation to the ceiling above the door is 59. If the ceiling is 9.8 feet above the floor, what is the vertical dimension of the door (Figure 17)? Figure 17 Height of Building A man standing on the roof of a building 600 feet high looks down to the building next door. He finds the angle of depression to the roof of that building from the roof of his building to be 34.5, while the angle of depression from the roof of his building to the bottom of the building next door is 63.2. How tall is the building next door?Height of an Obelisk Two people decide to find the height of an obelisk. They posit ion themselves 25 feet apart in line with, and on the same side of, the obelisk. If they find that the angles of elevation from the ground where they are standing to the top of the obelisk are 65 and 54, how tall is the obelisk?Distance In Figure 18, a person standing at point A notices that the angle of elevation to the top of the antenna is 47 30. A second person standing 33.0 feet farther from the antenna than the person at A finds the angle of elevation to the top of the antenna to be 42 10. How far is the person at A from the base of the antenna? Figure 18 Height of a Tree An ecologist wishes to find the height of a redwood tree that is on the other side of a creek, as shown in Figure 19. From point A he finds that the angle of elevation to the top of the tree is 10.7. He then walks 24.8 feet at a right angle from point A to point B. There he finds that the angle between AB and a line extending from B to the tree is 86.6. What is the height of the tree? Figure 19 Rescue A helicopter makes a forced landing at sea. The last radio signal received at station C gives the bearing of the helicopter from C as N 57.5 E at an altitude of 426 feet. An observer at C sights the helicopter and gives DCB as 12.3, how far will a rescue boat at A have to travel to reach any survivors at B (Figure 20)? Figure 20 Height of a Flagpole Two people decide to estimate the height of a flagpole. One person positions himself due north of the pole and the other person stands due cast of the pole. If the two people are the same distance from the pole and 25 feet from each other, find the height of the pole if the angle of elevation from the ground to the top of the pole at each persons position is 56 (Figure 21). Figure 21 Height of a Tree To estimate the height of a tree, one person positions himself due south of the tree, while another person stands due east of the tree, the two people are the same distance from the tree and 35 feet from each other, what is the height of the tree if the angle of elevation from the ground at each persons position to the top of the tree is 58?Radius of Earth A satellite is circling 112 miles above earth, as shown in Figure 22. When the satellite is directly above point B. angle A is found to be 76.6. Use this information to find the radius of earth. Figure 22 Distance Suppose Figure 22 is an exaggerated diagram of a plane flying above earth. If the plane is 4.55 miles above earth and the radius of earth is 3.960 miles, how far is it from the plane to the horizon? What is the measure of angle A? Figure 22 Distance A ship is anchored off a long straight shoreline that runs north and south. From Iwo observation points 15 miles apart on shore, the bearings of the ship are N 31 E and S 53 E. What is the shortest distance from the ship to the shore?Distance Pat and Tim position themselves 2.5 miles apart to watch a missile launch from Vandenberg Air Force Base. When the missile is launched, Pat estimates its bearing from him to be S 75 W, while Tim estimates the bearing of the missile from his position to be N 65 W. If Tim is due south of Pat, how far is Tim from the missile when it is launched?Spiral of Roots Figure 23 shows the Spiral of Roots we mentioned in the previous chapter. Notice that we have labeled the angles at the center of the spiral with 1,2,3, and so on. Figure 23 Find the values of 1, 2, and 3 accurate to the nearest hundredth of a degree.Spiral of Roots Figure 23 shows the Spiral of Roots we mentioned in the previous chapter. Notice that we have labeled the angles at the center of the spiral with 1,2,3, and so on. Figure 23 If n stands for the nth angle formed at the center of the Spiral of Roots, find a formula for sin n.One of the items we discussed in this section was topographic maps. The process of making one of these maps is an interesting one. It invokes aerial photography and different colored projections of the resulting photographs. Research the process used to draw the contour lines on a topographic map, and then give a detailed explanation of that process.Albert lives in New Orleans. At noon on a summer day, the angle of elevation of the sun is 84. The window in Alberts room is 4.0 feet high and 6.5 feet wide. (Sec Figure 24.) a. Calculate the area of the floor surface in Alberts room that is illuminated by the sun when the angle of elevation of the sun is 84. b. One winter day the angle of elevation of the sun outside Alberts window is 37. Will the illuminated area of the floor in Alberts room be greater on the summer day, or on the winter day? Figure 24 49PS 50PS 51PS 52PS 53PS Show that each of the following statements is true by transforming the left side of each one into the right side. (1cos)(1+cos)=sin2 55PS 56PS 57PS If the angle of elevation to the sun is 74.3 when a flagpole casts a shadow of 22.5 feet, what is the height of the flagpole? a. 63.2 feet b. 79.5 feet c. 83.1 feet d. 80.0 feet A ship is anchored off a long straight shoreline that runs north and south. From two observation points 4.5 miles apart on shore, the bearings of the ship arc S 73 W and N 17 W. What is the distance from the ship to the northernmost observation point? a. 4.3 mi b. 14.7 mi c. 4.7 mi d. 1.3 mi To estimate the height of a tree, one person stands due north of the tree and a second person stands due cast of the tree. If the two people are the same distance from the tree and 35 feet from each other, find the height of the tree if the angle of elevation from the ground to the top of the tree at each persons position is 65. a. 53ft b. 110 ft c. 75ft d. 130ft 1PS For Questions 1 through 8, fill in each blank with the appropriate word or expression. Two vectors are equivalent if they have the same _______ and _______.3PS 4PS For Questions 1 through 8, fill in each blank with the appropriate word or expression. Every vector V can be expressed as a sum. V=Vx+Vy, where Vx, is called the __________ vector _________ of V and V is called the _______ vector _________ of V.6PS 7PS 8PS Draw vectors representing the following velocities: 30mi/hr due north 10PS 11PS 12PS 13PS 14PS 15PS 16PS Bearing and Distance A person is riding in a hot air balloon. For the first hour the wind current is a constant 9.50 miles per hour in the direction N 37.5 E. Then the wind current changes to 8.00 miles per hour and heads the balloon in the direction S 52.5 E. If this continues for another 1.5 hours, how far is the balloon from its starting point? What is the bearing of the balloon from its starting point (Figure 20)? Figure 20 18PS 19PS 20PS 21PS 22PS 23PS 24PS 25PS 26PS 27PS For each problem below, the magnitudes of the horizontal and vertical vector components, and Vx and Vy of vector V are given. In each case find the magnitude of V. Vx=2.2,Vy=8.8 Navigation A ship is 2.8 off course. If the ship is traveling at 14.0 miles per hour, how far off course will it be after 2 hours?Navigation If a navigation error puts a plane 1.9 off course, how far off course is the plane after flying 135 miles?31PS 32PS 33PS 34PS Distance A ship travels 130 kilometers on a bearing of S 42 E. How far cast and how far south has it traveled?36PS Velocity of an Arrow An arrow is shot into the air so that its horizontal velocity is 35.0 feet per second and its vertical velocity is 15.0 feet per second (Figure 21). Find the velocity of the arrow. Figure 21 Velocity of an Arrow the horizontal and vertical components of the velocity of an arrow shot into the air are 16.5 feet per second and 24.3 feet per second, respectively. Find the velocity of the arrow.Distance A plane travels 170 miles on a bearing of N 18 E and then changes its course to N 49 E and travels another 120 miles. Find the total distance traveled north and the total distance traveled east.Distance A ship travels in the direction S 120 E for 68 miles and then changes its course to S 60 E and travels another 110 miles. Find the total distance south and the total distance east that the ship traveled.41PS 42PS Force An 8.0-pound weight is lying on a sit-up bench at the gym. If the bench is inclined at an angle of 15, there are three forces acting on the weight, as shown in Figure 22. N is called the normal force and it acts in the direction perpendicular to the bench. F is the force due to friction that holds the weight on the bench. If the light does not move, then the sum of these three forces is 0. Find the magnitude of N and the magnitude of F. Figure 22 Force Repeat Problem 43 for a 25.0-pound weight and a bench inclined at 12.5.45PS 46PS 47PS 48PS 49PS 50PS Draw 135 in standard position, locate a convenient point on the terminal side, and then find sin 135, cos 135, and tan 135.52PS 53PS 54PS 55PS 56PS 57PS 58PS 59PS 60PS Find sin A, cos A, tan A, and sin B, cos B, and tan B in right triangle ABC, with C=90 given the following information. a=1andb=2 2CT 3CT Use Definition II to explain why, for any acute angle , II is impossible for sin =2.Fill in the blank to make the statement true: sin 14 = cos ______.6CT 7CT 8CT 9CT 10CT 11CT 12CT Use a calculator to find the following. Round to four decimal places. sin2420 Use a calculator to find the following. Round to four decimal places. cos48.3 Use a calculator to find the following. Round to four decimal places. cot7120 Use a calculator to find to the nearest tenth of a degree if is an acute angle and satisfies the given statement. sin=0.6459 Use a calculator to find to the nearest tenth of a degree if is an acute angle and satisfies the given statement. sec=1.923 The following problems refer to right triangle ABC with C = 90. In each case, find all the missing parts. a=68.0 and b=104 19CT 20CT 21CT Geometry If the altitude of an isosceles triangle is 52 centimeters and each of the two equal angles measures 71, how long are the two equal sides?Angle of Elevation If the angle of elevation of the sun is 7530, how tall is a post that casts a shadow 1.5 feet long?Distance Two guy wires from the top of a 35-foot tent pole are anchored to the ground below by two stakes. The tent pole is perpendicular to the ground and between the two stakes. If the angles of depression from the top of the pole to each of the stakes are 47 and 43, how far apart are the stakes?25CT 26CT Distance and Bearing A ship travels 120 miles on a bearing of S 60 E. How far east and how far south has the ship traveled?Force Tyler and his cousin Kelly have attached a rope to the branch of a tree and tied a board to the other end to form a swing. Tyler sits on the board while his cousin pushes him through an angle of 25.5 and holds him there. If Tyler weighs 95.5 pounds, find the magnitude of the force Kelly must push with horizontally to keep Tyler in static equilibrium. See Figure 1. Figure 1 29CT 30CT 1GP Use your knowledge of a 306090 triangle to find sides g and h.3GP 4GP 5GP 6GP The origins of the sine function are found in the tables of chords for a circle constructed by the Greek astronomers/mathematicians Hipparchus and Ptolemy. However, the origins of the tangent and cotangent functions lie primarily with Arabic and Islamic astronomers. Called the umbra recta and umbra versa, their connection was not to the chord of a circle but to the gnomon of a sundial. Research the origins of the tangent and cotangent functions. What was the connection to sundials? What other contributions did Arabic astronomers make to trigonometry? Write a paragraph or two about your findings.For Questions 1 through 3, fill in each blank with the appropriate word or symbol. For an angle in standard position, the ____________ angle is the positive acute angle between the terminal side of and the _-axis.For Questions 1 through 3, fill in each blank with the appropriate word or symbol. The only possible difference between a trigonometric function of an angle and its reference angle will be the _____ of the value.For Questions 1 through 3, fill in each blank with the appropriate word or symbol. To find a reference angle using the sin1, cos1, or tan1 keys on a calculator, always enter a _____ value.Complete each statement regarding an angle and its reference angle . If QI, then =. If QII, then =. If QIII, then =. If QIV, then =.Draw each of the following angles in standard position and then name the reference angle. 150 Draw each of the following angles in standard position and then name the reference angle. 210 Draw each of the following angles in standard position and then name the reference angle. 253.8 Draw each of the following angles in standard position and then name the reference angle. 143.4 9PS Draw each of the following angles in standard position and then name the reference angle. 93.2 11PS Draw each of the following angles in standard position and then name the reference angle. 17140 13PS 14PS 15PS 16PS 17PS 18PS Find the exact value of each of the following. sin210

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