Bartleby Sitemap - Textbook Solutions
All Textbook Solutions for Trigonometry (MindTap Course List)
1PSFor Questions 1 through 7, fill in each blank with the appropriate word or number. Two angles with a sum of 90 are called ___________________ angles, and when the sum is 180 they are called ______________________ angles.For Questions 1 through 7, fill in each blank with the appropriate word or number. In any triangle, the sum of the three interior angles is always ______.For Questions 1 through 7, fill in each blank with the appropriate word or number. In a right triangle, the longest side opposite the right angle is called the __________________ and the other two sides are called ___________________.5PSFor Questions 1 through 7, fill in each blank with the appropriate word or number. In a 306090 triangle, the hypotenuse is always ______________ the shortest side, and the side opposite the 60 angle is always _________________ times the shortest side.For Questions 1 through 7, fill in each blank with the appropriate word or number. In a 454590 triangle, the legs are always __________________ and the hypotenuse is always __________________ times either leg.Match each term with the appropriate angle measure. a. Right. i. 090 b. Straight ii. =90 c. Acute iii. 90180 d. Obtuse iv. =180Indicate which of the angles below are acute angles and which are obtuse angles. Then give the complement and the supplement of each angle. 10Indicate which of the angles below are acute angles and which are obtuse angles. Then give the complement and the supplement of each angle. 70Indicate which of the angles below are acute angles and which are obtuse angles. Then give the complement and the supplement of each angle. 45Indicate which of the angles below are acute angles and which are obtuse angles. Then give the complement and the supplement of each angle. 90Indicate which of the angles below are acute angles and which are obtuse angles. Then give the complement and the supplement of each angle. 120Indicate which of the angles below are acute angles and which are obtuse angles. Then give the complement and the supplement of each angle. 150Indicate which of the angles below are acute angles and which are obtuse angles. Then give the complement and the supplement of each angle. x16PSProblems 17 through 22 refer to Figure 19. (Remember: The sum of the three angles in any triangle is always 180.) Figure 19 Find if A=30.Problems 17 through 22 refer to Figure 19. (Remember: The sum of the three angles in any triangle is always 180.) Figure 19 Find if =50.Problems 17 through 22 refer to Figure 19. (Remember: The sum of the three angles in any triangle is always 180.) Figure 19 Find if A=2.Problems 17 through 22 refer to Figure 19. (Remember: The sum of the three angles in any triangle is always 180.) Figure 19 Find if A=.Problems 17 through 22 refer to Figure 19. (Remember: The sum of the three angles in any triangle is always 180.) Figure 19 Find A if B=30 and +=100.Problems 17 through 22 refer to Figure 19. (Remember: The sum of the three angles in any triangle is always 180.) Figure 19 Find B if +=75 and A=50.Figure 20 shows a walkway with a handrail. Angle is the angle between the walkway and the horizontal, while angle is the angle between the vertical posts of the handrail and the walkway. Use Figure 20 to work Problems 23 through 26. (Assume that the vertical posts arc perpendicular to the horizontal.) Figure 20 Are angles and complementary or supplementary angles?Figure 20 shows a walkway with a handrail. Angle is the angle between the walkway and the horizontal, while angle is the angle between the vertical posts of the handrail and the walkway. Use Figure 20 to work Problems 23 through 26. (Assume that the vertical posts arc perpendicular to the horizontal.) Figure 20 If we did not know that the vertical posts were perpendicular to the horizontal, could we answer Problem 23?Figure 20 shows a walkway with a handrail. Angle is the angle between the walkway and the horizontal, while angle is the angle between the vertical posts of the handrail and the walkway. Use Figure 20 to work Problems 23 through 26. (Assume that the vertical posts arc perpendicular to the horizontal.) Figure 20 Find if =50.Figure 20 shows a walkway with a handrail. Angle is the angle between the walkway and the horizontal, while angle is the angle between the vertical posts of the handrail and the walkway. Use Figure 20 to work Problems 23 through 26. (Assume that the vertical posts arc perpendicular to the horizontal.) Figure 20 Find if =15.27PS28PSGeometry An isosceles triangle is a triangle in which two sides are equal in length. The angle between the two equal sides is called the vertex angle, while the other to angles are called the base angles. If the vertex angle is 40, what is the measure of the base angles?30PSProblems 31 through 36 refer to right triangle ABC with C=90. If a=4 and b=3, find c.Problems 31 through 36 refer to right triangle ABC with C=90. If a=2 and c=10, find b.Problems 31 through 36 refer to right triangle ABC with C=90. If a=8 and c=17, find b.34PS35PS36PSSolve for x in each of the following right triangles:38PSSolve for x in each of the following right triangles:Solve for x in each of the following right triangles:Solve for x in each of the following right triangles:Solve for x in each of the following right triangles:Problems 43 and 44 refer to Figure 21. Figure 21 Find AB if BC=4,BD=5, and AD=2.Problems 43 and 44 refer to Figure 21. Figure 21 Find BD if BC=5 , AB=13, and AD=4.Problems 45 and 46 refer to Figure 22, which shows a circle with center at C and a radius of r, and right triangle ADC. Figure 22 Find r if AB=4 and AD=8.Problems 45 and 46 refer to Figure 22, which shows a circle with center at C and a radius of r, and right triangle ADC. Figure 22 Find AB if r = 5 and AD = 12.Pythagorean Theorem The roof of a house is to extend up 13.5 feet above the ceiling, which is 36 feet across, forming an isosceles triangle (Figure 23). Find the length of one side of the roof. Figure 23Surveying A surveyor is attempting to find the distance across a pond. From a point on one side of the pond he walks 25 yards to the end of the pond and then makes a 90 turn and walks another 60 yards before coming to a point directly across the pond from the point at which he started. What is the distance across the pond? (See Figure 24.) Figure 24Find the remaining sides of a 306090 triangle if the shortest side is 1.Find the remaining sides of a 306090 triangle if the shortest side is 451PSFind the remaining sides of a 306090 triangle if the longest side is 5Find the remaining sides of a 306090 triangle if the side opposite 60 is 654PSEscalator An escalator in a department store is to carry people a vertical distance of 20 feet between floors. How long is the escalator if it makes an angle of 30 with the ground?Escalator What is the length of the escalator in Problem 55 if it makes an angle of 60 with the ground?57PSProblems 57 and 58 refer to the two-person tent shown in Figure 25. Assume the tent has a floor and is closed at both ends. Give your answers in exact form and also approximate to the nearest tenth of a unit. Figure 25 Tent Design If the height h at the center of the tent is to be 3 feet and 90 square feet of material are available to make the tent, how long should the tent be?Find the remaining sides of a 454590 triangle if the shorter sides are each 4560PSFind the remaining sides of a 454590 triangle if the longest side is 8262PS63PSFind the remaining sides of a 454590 triangle if the longest side is 12Distance a Bullet Travels A bullet is tired into the air at an angle of 45. How far does it travel before it is 1,000 feet above the ground? (Assume that the bullet travels in a straight line; neglect the forces of gravity, and give your answer to the nearest foot.)Time a Bullet Travels If the bullet in Problem 65 is traveling at 2,828 feet per second, how long does it take for the bullet to reach a height of 1,000 feet?67PS68PSGeometry: Characteristics of a Cube The object shown in Figure 27 is a cube (all edges are equal in length). Use this diagram for Problems 69 through 72. Figure 27 If the length of each edge of the cube is 1 inch, find a. the length of diagonal CH b. the length of diagonal CFGeometry: Characteristics of Cube The object shown in Figure 27 is a cube (all edges are equal in length). Use this diagram for Problems 69 through 72. Figure 27 If the length of diagonal GD is 5 centimeters, find a. the length of each side b. the length of diagonal GB71PSGeometry: Characteristics of a Cube The object shown in Figure 27 is a cube (all edges are equal in length). Use this diagram for Problems 69 through 72. Figure 27 What is the measure of GDH?The Spiral of Roots The introduction to this chapter shows the Spiral of Roots. The following three figures (Figures 28, 29, and 30) show the first three stages in the construction of the Spiral of Roots. Using graph paper and a ruler, construct the Spiral of Roots, labeling each diagonal as you draw it, to the point where you can see a line segment with a length of 10.The Golden Ratio Rectangle ACEF (Figure 31) is a golden rectangle. It is constructed from square ACDB by holding line segment OB fixed at point O and then letting point B drop down until OB aligns with CD. The ratio of the length to the width in the golden rectangle is called the golden ratio. Find the lengths below to arrive at the golden ratio. a. Find the length of OB. b. Find the length of OE. c. Find the length of CE. d. Find the ratio CFEF Figure 31Compute the complement and supplement of 61. a. Complement = -61, supplement = 119 b. Complement = -61, supplement = 299 c. Complement = 119, supplement = 29 d. Complement = 29, supplement = 11976PS77PSAn escalator in a department store makes an angle of 45 with the ground. How long is the escalator if it carries people a vertical distance of 24 feet? a. 122ft b. 242ft c. 83ft d. 48 ftFor Questions 1 through 6, fill in each blank with the appropriate word or expression. The Cartesian plane is divided into four regions, or ___________, numbered through __________________ in a _________________ direction.2PS3PSFor Questions 1 through 6, fill in each blank with the appropriate word or expression. The notation QIII means that is in standard position and its ________ side lies in ________ ________.5PS6PSState the formula for the distance between (x1, y1) and (x2, y2).8PS9PS10PS11PSDetermine which quadrant contains each of the following points. (1,3)13PSGraph each of the following lines. y=x15PS16PS17PS18PSFor points (x. y) in quadrant I the ratio x/y is always positive because x and y are always positive. In what other quadrant is the ratio x/y always positive?20PSGraph each of the fo1lowing parabolas. y=x2422PS23PS24PSUse your graphing calculator to graph y=ax2 for a=110,15,1,5, and 10. Copy all five graphs onto a single coordinate system and label each one. What happens to the shape of the parabola as the value of a gets close to zero? What happens to the shape of the parabola when the value of a gets large?26PSUse your graphing calculator to graph y=(xh)2 for h = –3.0, and 3. Copy all three graphs onto a single coordinate system, and label each one. What happens to the position of the parabola when h0 ? What if h0?Use your graphing calculator to graph y=x2+k for k=3,0, and 3. Copy all three graphs onto a single coordinate system, and label each one. What happens to the position of the parabola when k < 0? What if k > 0?29PSHuman Cannonball Referring to Problem 29, find the height reached by the human cannonball after he has traveled 40 feet horizontally, and after he has traveled 140 feet horizontally. Verify that your answers are correct using your graphing calculator.31PS32PS33PS34PS35PS36PS37PSFind the distance from the origin out to the point (–5, 5).39PS40PSPythagorean Theorem An airplane is approaching Los Angeles International Airport at an altitude of 2,640 feet. If the horizontal distance from the plane to the runway is 1.2 miles, use the Pythagorean Theorem to find the diagonal distance from the plane to the runway (Figure 22). (5,280 feet equals 1 mile.) Figure 22Softball Diamond In softball, the distance from home plate to first base is 60 feet, as is the distance from first base to second base. If the lines joining home plate to first base and first base o second base form a right angle, how far does a catcher standing on home plate have to throw the ball so that it reaches the shortstop standing on second base (Figure 23)? Figure 23Softball and Rectangular Coordinates If a coordinate system is superimposed on the softball diamond in Problem 42 with the x-axis along the line from home plate to first base and the y-axis on the line from home plate to third base, what would be the coordinates of home plate, first base, second base, and third base?Softball and Rectangular Coordinates If a coordinate system is superimposed on the softball diamond in Problem 42 with the origin on home plate and the positive x-axis along the line joining home plate to second base, what would be the coordinates of first base and third base?45PS46PS47PS48PS49PS50PS51PSGraph the circle x2+y2=1 with your graphing calculator. Use the feature on your calculator that allows you to evaluate a function from the graph to find the coordinates of all points on the circle that have the given x-coordinate. Write your answers as ordered pairs and round to four places past the decimal point when necessary. x=14Graph the circle x2+y2=1 with your graphing calculator. Use the feature on your calculator that allows you to evaluate a function from the graph to find the coordinates of all points on the circle that have the given x-coordinate. Write your answers as ordered pairs and round to four places past the decimal point when necessary. x=2254PS55PS56PS57PSUse the graph of Problem 50 to name the points at which the line x – y = 6 will intersect the circle x2+y2=36.59PS60PS61PS62PS63PS64PS65PS66PS67PS68PSUse Figure 24 for Problems 61 through 72. Figure 24 Name an angle between 0 and 360 that is coterminal with each of the following angles. 13570PSUse Figure 24 for Problems 61 through 72. Figure 24 Name an angle between 0 and 360 that is coterminal with each of the following angles. 21072PSDraw each of the following angles in standard position, and find one positive angle and one negative angle that is coterminal with the given angle. 30074PS75PS76PSDraw each of the following angles in standard position and then do the following: a. Name a point on the terminal side of the angle. b. Find the distance from the origin to that point. c. Name another angle that is coterminal with the angle you have drawn. 13578PSDraw each of the following angles in standard position and then do the following: a. Name a point on the terminal side of the angle. b. Find the distance from the origin to that point. c. Name another angle that is coterminal with the angle you have drawn. 225Draw each of the following angles in standard position and then do the following: a. Name a point on the terminal side of the angle. b. Find the distance from the origin to that point. c. Name another angle that is coterminal with the angle you have drawn. 31581PS82PS83PSDraw each of the following angles in standard position and then do the following: a. Name a point on the terminal side of the angle. b. Find the distance from the origin to that point. c. Name another angle that is coterminal with the angle you have drawn. 9085PSFind all angles that are coterminal with the given angle. 6087PSFind all angles that are coterminal with the given angle. 180Draw 30 in standard position. Then find a if the point (a, 1) is on the terminal side of 30.Draw 60 in standard position. Then find b if the point (2, b) is on the terminal side of 60.Draw an angle in standard position whose terminal side contains the point (3, –2). Find the distance from the origin to this point.Draw an angle in standard position whose terminal side contains the point (2, –3). Find the distance from the origin to this point.93PS94PS95PS96PS97PS98PSTo draw 140 in standard position, place the vertex at the origin and draw the terminal side 140 ______ from the _________________ a. clockwise, positive x-axis b. counterclockwise, positive x-axis c. counterclockwise, positive y -axis d. clockwise, positive y-axisWhich angle is coterminal with 160 ? a. 50 b. –70 c. 20 d. –200For Questions 1 and 2, fill in each blank with the appropriate word or number. In Definition I, (x, y) is any point on the __________ side of when in standard position, and r is the ____________ from the ________ to (x, y).2PS3PSWhich of the six trigonometric functions do not depend on the value of r?Find all six trigonometric functions of if the given point is on the terminal side of . (In Problem 15. assume that a is a positive number.) (3, 4)6PS7PS8PS9PS10PSFind all six trigonometric functions of if the given point is on the terminal side of . (In Problem 15, assume that a is a positive number.) (3,1)Find all six trigonometric functions of if the given point is on the terminal side of . (In Problem 15, assume that a is a positive number.) (2,5)13PS14PS15PS16PSIn the following diagrams, angle is in standard position. In each case, find sin , cos , and tan .In the following diagrams, angle is in standard position. In each case, find sin , cos , and tan .In the following diagrams, angle is in standard position. In each case, find sin , cos , and tan .20PSUse your calculator to find sin and cos if the point (9.36, 7.02) is on the terminal side of .22PSDraw each of the following angles in standard position, find a point on the terminal side, and then find the sine, cosine, and tangent of each angle: 135Draw each of the following angles in standard position, find a point on the terminal side, and then find the sine, cosine, and tangent of each angle: 225Draw each of the following angles in standard position, find a point on the terminal side, and then find the sine, cosine, and tangent of each angle: 9026PS27PSDraw each of the following angles in standard position, find a point on the terminal side, and then find the sine, cosine, and tangent of each angle: 9029PSDraw each of the following angles in standard position, find a point on the terminal side, and then find the sine, cosine, and tangent of each angle: 135Determine whether each statement is true or false. cos35cos4532PS33PS34PSExplain why there is no angle such that sin = 2.Explain why there is no angle such that sec =12.37PSWhy is sin 1 for any angle in standard position?As increases from 0 to 90, the value of sin tends toward what number?40PSAs increases from 0 to 90, the value of tan tends toward ___________.As increases from 0 to 90, the value of csc tends toward _______.43PS44PSIndicate the two quadrants could terminate in given the value of the trigonometric function. cos=0.4546PSIndicate the two quadrants could terminate in given the value of the trigonometric function. tan=724Indicate the two quadrants could terminate in given the value of the trigonometric function. cot=2120Indicate the two quadrants could terminate in given the value of the trigonometric function. csc=2.4550PS51PS52PSIndicate the quadrants in which the terminal side of must lie under each of the following conditions. sin and tan have the same signIndicate the quadrants in which the terminal side of must lie under each of the following conditions. csc and cot have the same sign55PSFor Problems 55 through 68, find the remaining trigonometric functions of based on the given information. cos=2425 and terminates in QIVFor Problems 55 through 68, find the remaining trigonometric functions of based on the given information. cos=2029 and terminates in QIIFor Problems 55 through 68, find the remaining trigonometric functions of based on the given information. sin=2029 and terminates in QIIIFor Problems 55 through 68, find the remaining trigonometric functions of based on the given information. cos=32 and terminates in QIVFor Problems 55 through 68, find the remaining trigonometric functions of based on the given information. sin=22 and terminates in QII61PSFor Problems 55 through 68, find the remaining trigonometric functions of based on the given information. tan=3 and terminates in QIV63PS64PS65PS66PSFor Problems 55 through 68, find the remaining trigonometric functions of based on the given information. tan=ab where a and b are both positiveFor Problems 55 through 68, find the remaining trigonometric functions of based on the given information. cot=mn where m and n are both positive69PS70PSFind sin and cos if the terminal side of lies along the line y=2x in QI.Find sin and cos if the terminal side of lies along the line y=12x QIII.Find sin and tan if the terminal side of lies along the line y=3x in QII.Find sin and tan if the terminal side of lies along the line y=3x in QIV.75PS76PS77PS78PSFind cos if (1, –3) is a point on the terminal side of . a. 22 b. 13 c. 31010 d. 101080PS81PSFind tan if sin =45 and terminates in QII. a. 43 b. 35 c. 53 d. 34For Questions 1 and 2, fill in each blank with the appropriate word or expression. An identity is an equation that is _____________________ for all replacements of the variable for which it is _________.For Questions 1 and 2, fill in each blank with the appropriate word or expression. The notation cos2 is a shorthand for ( _________________ )2.Match each trigonometric function with its reciprocal. a. sine i. cotangent b. cosine ii. cosecant c. tangent iii. secantMatch the trigonometric functions that are related through a Pythagorean identity. a. sine i. secant b. tangent ii. cosecant c. cotangent iii. cosine5PS6PS7PS8PS9PS10PSGive the reciprocal of each number. x12PS13PS14PSUse the reciprocal identities for the following problems. If sec=2, find cos.16PSUse the reciprocal identities for the following problems. If tan=a(a0), find cot.18PSUse a ratio identity to find tan given the following values. sin=255 and cos=5520PSUse a ratio identity to find tan given the following values. sin=513 and cos=121322PSFor Problems 23 through 26, recall that sin2 means (sin)2. If sin=22, find sin2.24PSFor Problems 23 through 26, recall that sin2 means (sin)2. If tan=2, find tan3.26PS27PS28PS29PSFor Problems 27 through 30, let sin=12/13, and cos=5/13, and find the indicated value. csc31PS32PSUse the equivalent forms of the first Pythagorean identity on Problems 31 through 38. Find cos if sin=32 and terminates in QII.Use the equivalent forms of the first Pythagorean identity on Problems 31 through 38. Find cos if sin=14 and terminates in QIII.Use the equivalent forms of the first Pythagorean identity on Problems 31 through 38. If sin=45 and terminates in QIII, find cos.Use the equivalent forms of the first Pythagorean identity on Problems 31 through 38. If sin=513 and terminates in QIV, find cos.Use the equivalent forms of the first Pythagorean identity on Problems 31 through 38. If cos=32 and terminates in QI, find sin.Use the equivalent forms of the first Pythagorean identity on Problems 31 through 38. If cos=22 and terminates in QII, find sin .Find tan if sin=13 and terminates in QI.Find cot if cot=23 and terminates in QII.