Bartleby Sitemap - Textbook Solutions
All Textbook Solutions for Calculus: An Applied Approach (MindTap Course List)
2CP3CP4CP5CP6CP7CP1SWU2SWU3SWU4SWU5SWU6SWU7SWU8SWU9SWU10SWU11SWU12SWU1E2EEvaluating Trigonometric Functions In Exercises 1-6, find the exact values of the six trigonometric functions of the angle . See Example 1.Evaluating Trigonometric Functions In Exercises 1-6, find the exact values of the six trigonometric functions of the angle . See Example 1.5EEvaluating Trigonometric Functions In Exercises 1-6, find the exact values of the six trigonometric functions of the angle . See Example 1.7E8E9E10E11E12E13E14E15E16E17E18E19E20E21E22E23EEvaluating Trigonometric Functions In Exercises 19-32, evaluate the six trigonometric functions of the angle without using a calculator. See Examples 2 and 3. 15025E26E27EEvaluating Trigonometric Functions In Exercises 19-32, evaluate the six trigonometric functions of the angle without using a calculator. See Examples 2 and 3. 36029E30E31E32E33E34E35E36E37E38E39E40E41E42E43E44E45E46ESolving a Right Triangle In Exercises 43-48, solve for x, y, or r as indicated. See Solve for y.48E49E50E51E52E53E54E55E56E57E58E59E60E61E62E63E64E65E66E67E68E69E70ELength A 20-foot ladder leaning against the side of a house makes a 75 angle with the ground (see figure). How far up the side of the house does the ladder reach?Width of a River A biologist wants to know the width w of a river in order to set instruments to study the pollutants in the water. From point A, the biologist walks upstream 100 feet and sights to point C. From this sighting it is determined that = 50 (see figure). How wide is the river?Distance An airplane flying at an altitude of 6 miles is on a flight path that passes directly over an observer (see figure). Let be the angle of elevation from the observer to the plane. Find the distance d from the observer to the plane when (a) = 30, (b) = 60, and (c) = 90.Skateboard Ramp A skateboard ramp with a height of 4 feet has an angle of elevation of 18 (see figure). What is the length c of the skateboard ramp?Height A 25-meter line is used to tether a helium-filled balloon to the ground. Because of a breeze, the line makes an angle of approximately 75 with the ground. (a) Draw the right triangle that gives a visual representation of the problem. Show the known side lengths and angles of the triangle and use a variable to indicate the height of the balloon. (b) Use a trigonometric function to write an equation involving the unknown quantity. (c) What is the height of the balloon?Empire State Building You are standing 45 meters from the base of the Empire State Building. You estimate that the angle of elevation to the top of the 86th floor is 82. The total height of the building is another 123 meters above the 86th floor. (a) What is the approximate height of the building? (b) One of your friends is on the 86th floor. What is the distance between you and your friend?77E78EHeight of a Mountain In traveling across flat land, you notice a mountain directly in front of you. Its angle of elevation (to the peak) is 3.5. After you drive 13 miles closer to the mountain, the angle of elevation is 9 (see figure). Approximate the height of the mountain.80EMedicine The temperature T (in degrees Fahrenheit) of a patient t hours after arriving at the emergency room of a hospital at 10:00 p.m. is given by T(t)=98.6+4cost36,0t18. Find the patients temperature at (a) 10:00 p.m., (b) 4:00 a.m., and (c) 10:00 a.m. (d) At what time do you expect the patients temperature to return to normal (98.6) ? Explain your reasoning.82E83E84E85E86E87E88E1CP2CP3CP4CP5CP6CP1SWU2SWU3SWU4SWU5SWU6SWU7SWU8SWU9SWU10SWU11SWU12SWU13SWU14SWU15SWU16SWU17SWU18SWU1E2E3E4E5E6EFinding the Period and Amplitude In Exercises 1-14, find the period and amplitude of the trigonometric function. y=sin3x8E9E10E11E12E13E14E15E16EFinding the Period In Exercises 15-20, find the period of the trigonometric function. y=3sec5x18E19E20E21E22E23EMatching In Exercises 21-26, match the trigonometric function with the correct graph and give the period of the function. [The graphs are labeled (a)-(f).] y=secx25E26E27E28E29E30E31E32E33E34E35E36E37E38E39E40E41E42E43E44E45E46E47E48E49E50E51E52E53E54E55E56E57E58E59E60E61E62EGraphical Reasoning In Exercises 63-66, find a and d for the function f(x)=acosx+d such that the graph of f matches the figure.64EGraphical Reasoning In Exercises 63-66, find a and d for the function f(x)=acosx+d such that the graph of f matches the figure.Graphical Reasoning In Exercises 63-66, find a and d for the function f(x) = a cos x + d such that the graph of f matches the figure.67E68E69E70E71E72E73EBiology: Predator-Prey Cycle The population P of a predator at time t (in months) is modeled by P=5700+1200sin2t24 and the population p of its prey is modeled by p=9800+2750cos2t24. (a) Use a graphing utility to graph both models in the same viewing window. (b) Explain the oscillations in the size of each population.Music When tuning a piano, a technician strikes a tuning fork for the A above middle C and sets up wave motion that can be approximated by y = 0.001 sin 880t where t is the time (in seconds). (a) Find the amplitude and range of the function. (b) Find the period p of the function. (c) What is the frequency f of this note ( f = 1/p)? (d) Use a graphing utility to graph the function.Health The function P=10020cos5t3 approximates the blood pressure P (in millimeters of mercury) at time t (in seconds) for a person at rest. (a) Find the amplitude of the function. (b) Find the period of the function. (c) What are the maximum and minimum blood pressures? (d) Find the number of heartbeats per minute, which is the number of cycles per minute. (e) Use a graphing utility to graph the pressure function.77E78E79E80E81E82E83EHOW DO YOU SEE IT? The normal monthly high temperatures for Erie, Pennsylvania, are approximated by H(t)=56.72+23.62sin(0.50t2.08) and the normal monthly low temperatures for Erie, Pennsylvania, are approximated by L(t)=41.89+21.52sin(0.52t2.27) where t is the time (in months), with t = 1 corresponding to January. (Source: National Climatic Data Center) (a) During what part of the year is the difference between the normal high and low temperatures greatest? When is it least? (b) The sun is the farthest north in the sky around June 21, but the graph shows the highest temperatures at a later date. Approximate the lag time of the temperatures relative to the position of the sun.True or False? In Exercises 8588, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. The amplitude of f(x)=3cos2xis3.86E87E88E1QY2QY3QY4QY5QY6QY7QY8QY9QY10QY11QY12QY13QYIn Exercises 914, evaluate the trigonometric function without using a calculator. csc3215QY16QYIn Exercises 15-17, solve the equation for . Assume 02. sin2=3cos218QY19QY20QYA map maker needs to determine the distance d across a small lake. The distance from point A to point B is 500 feet and the angle is 35 (see figure). What is the distance across the small lake?22QY23QY24QY25QYDifferentiate each function. a. y=cos4x b. y=sin(x21) c. y=tanx22CP3CP4CP5CP6CP7CP8CP9CP1SWU2SWU3SWU4SWU5SWU6SWU7SWU8SWUIn Exercises 7-10, solve the equation for x. Assume 0x2. tanx=3310SWU1E2E3E4E5E6E7E8E9E10E11E12E13E14E15E16E17E18E19E20E21E22E23E24E25E26E27E28E29E30E31E32E33E34EDifferentiating Trigonometric Functions In Exercises 29-40, find the derivative of the function and simplify your answer by using the trigonometric identities listed in Section 8.2. y=tanxx36E37E38E