5.6 Inverse Trigonometric Functions: Differentiation 329
5.6 Inverse Trigonometric Functions: Differentiation
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Evaluate the expression without using a calculator.
a. 0
b.
c.
d.
e.
____ 2. Evaluate the expression without using a calculator.
a.
b.
c.
d.
e.
____ 3. Evaluate the expression without using a calculator.
a.
b.
c. 3
d. 5
e. 4
330 Chapter 5: Logarithmic, Exponential, and Other Transcendental Functions
____ 4. Write the following expression in algebraic form.
a.
b.
c.
d.
e.
____ 5. Write the following expression in algebraic form.
a.
b.
c.
d.
e.
____ 6. Solve the following equation for .
a.
b.
c.
d.
e.
5.6 Inverse Trigonometric Functions: Differentiation 331
____ 7. Solve the following equation for .
a.
b.
c.
d.
e.
____ 8. Find the derivative of the function .
a.
b.
c.
d.
e.
332 Chapter 5: Logarithmic, Exponential, and Other Transcendental Functions
____ 9. Find the derivative of the function .
a.
b.
c.
d.
e.
____ 10. Find the derivative of the function .
a.
b.
c.
d.
e.
____ 11. Find the derivative of the function .
a.
b.
c.
d.
e.
5.6 Inverse Trigonometric Functions: Differentiation 333
____ 12. Find the derivative of the function .
a.
b.
c.
d.
e.
____ 13. Find an equation of the tangent line to the graph of at the point
.
a.
b.
c.
d.
e.
334 Chapter 5: Logarithmic, Exponential, and Other Transcendental Functions
____ 14. Find the slope-intercept form of the equation of the line tangent to the graph of
.
a.
b.
c.
d.
e.
____ 15. An airplane flies at an altitude of 14 miles toward a point directly over an observer.
Consider and x as shown in the following figure. Write as a function of x.
a.
b.
c.
d.
e.
5.6 Inverse Trigonometric Functions: Differentiation 335
____ 16. An airplane flies at an altitude of 6 miles towards a point directly over an observer.
Consider and x as shown in the following figure. The speed of the plane is 400 miles per hour. Find
when . Round your answer to three decimal places.
a. –17.647 rad/hr
b. 2.941 rad/hr
c. 17.647 rad/hr
d. 0.044 rad/hr
e. –8.824 rad/hr
____ 17. In a free-fall experiment, an object is dropped from a height of 256 feet. A camera on
the ground 500 feet from the point of impact records the fall of the object as shown in the figure.
Assuming the object is released at time t = 0. At what time will the object reach the ground level?
a. 3 seconds
b. 6 seconds
c. 7 seconds
d. 5 seconds
e. 4 seconds
336 Chapter 5: Logarithmic, Exponential, and Other Transcendental Functions
____ 18. In a free-fall experiment, an object is dropped from a height of 144 feet. A camera on
the ground 500 feet from the point of impact records the fall of the object as shown in the figure.
Assuming the object is released at time t = 0. Find the rate of change of the angle of elevation of the
camera when . Round your answer to four decimal places.
a. –0.6006 rad/sec
b. –0.0581 rad/sec
c. 0.0601 rad/sec
d. 0.0581 rad/sec
e. –0.0601 rad/sec
____ 19. An 85-foot billboard is perpendicular to a straight road and is 50 feet from the road as
shown in the figure. Find the point on the road such that the angle subtended by the billboard is a
maximum. How far is this point from the point on the road directly across from the billboard (in
feet)? Round your answer to two decimal places.
5.6 Inverse Trigonometric Functions: Differentiation 337
a. 50.00 ft
b. 29.41 ft
c. 41.08 ft
d. 82.16 ft
e. 85.00 ft
____ 20. A petrol car is parked 40 feet from a long warehouse (see figure). The revolving light
on top of the car turns at a rate of 30 revolutions per minute. Write as a function of x.
a.
b.
c.
d.
e.
338 Chapter 5: Logarithmic, Exponential, and Other Transcendental Functions
____ 21. A petrol car is parked 50 feet from a long warehouse (see figure). The revolving light
on top of the car turns at a rate of 30 revolutions per minute. How fast is the light beam moving along
the wall when the beam makes an angle of with the perpendicular from the light to the wall.
a.
b.
c.
d.
e.
5.6 Inverse Trigonometric Functions: Differentiation 339
5.6 Inverse Trigonometric Functions: Differentiation
Answer Section