12-6 Practice Day III

NAME DATE PERIOD

12-6 Practice Day III

Circular Functions

The terminal side of angle θ in standard position intersects the unit circle at each point P . Find cos θ and sin θ.

1. P-12, 32 2. P2029, -2129 3. P(0.8, 0.6 )

4. P (0, –1) 5. P-22, -22 6. P32, -12

Determine the period of each function

7. 8.

Find the exact value of each function.

9. cos 7π4 10. sin (–30°) 11. sin -2π3 12. cos (–330°)

13. cos 600° 14. sin 9π2 15. cos 7π 16. cos -11π4

17. sin (–225°) 18. sin 585° 19. cos -10π3 20. sin 840°

21. FERRIS WHEELS A Ferris wheel with a diameter of 100 feet completes 2.5 revolutions per minute. What is the period of the function that describes the height of a seat on the outside edge of the Ferris wheel as a function of time?

22. The Great Laxey wheel, located on the Isle of Man, is one of the largest working water heels in the world. The wheel was built in 1854 to pump water from the mines underneath it. The height h (in feet) above the viewing platform of a bucket on the wheel can be approximated by the function h=36.25sinπ12t+34.25.

a. In the first cycle what is the maximum height?

b. When does the wheel reach the maximum the first two times?

c. When is the first time the wheel is under water? How often does it happen?

23. A tornado siren makes 2.5 rotations per minute and the beam of sound has a radius of 1 mile. Ms. Miller’s house is 1 mile from the siren. The distance of the sound beam from her house varies periodically as a function of time.

a. Identify the period of the function in seconds.

b. Sketch a graph and write a function. Let the horizontal axis represent the time t from 0 to 60 seconds. Let the vertical axis represent the distance d the sound beam is from Ms. Miller’s house at a time t.

24. A Ferris wheel in China has a diameter of approximately 520 feet The height of a compartment h is a function of time t. It takes about 30 seconds to make one complete revolution. Let the height at the center of the wheel represent the height at a time 0. Sketch a graph and write a function.

Chapter 12 38 Glencoe Algebra 2