POD: Inverse Trig



Evaluating Inverse Trig Functions

Chapter 4.9

Honors Pre-Calculus

Find the following using the unit circle:

1. arccos -½

2. arctan 1

3. arcsin -½

4. arccos 0

5. arctan -[pic]

6. tan-1 (-1)

7. cos-1 [pic]

8. sin-1 [pic]

9. arctan[pic]

10. cos(arccos ½)

11. sin[cos-1 (-½)]

12. tan[sin-1 (1)]

13. sin[tan-1[pic]]

14. cos(sin-1 -1)

15. tan(cos-1 0)

Find the following by drawing a right triangle:

16. sin(arctan 4/5)

17. sec(arcsin 7/5)

18. cos(arcsin -48/50)

19. csc[arctan(-24/10)]

20. sec[arctan(-3/4)]

21. sin[arccos(-2/7)]

22. cot(arctan 16/13)

23. sin[arcsin(-6/10)]

24. tan(arctan 7)

25. cos(tan-1 2)

Answer the following:

26. An anchored barge bobs up and down with the height h of its transmitter (in feet) above sea level modeled by h = a sin bt + 12. During a large storm its height varies from 3 ft to 21 ft and there are 8.4 sec from one 21-ft height to the next. What are the values of the constants a and b?

27. On a particular Labor Day, the high tide in southern California occurs at 7:12 a.m. At that time you measure the water at the end of the Santa Monica Pier to be 11 ft deep. At 1:24 p.m. it is low tide, and you measure the water to be only 7 ft deep. Assume the depth of the water is a sinusoidal function of time with a period of ½ a lunar day, which is about 12 h 24 min.

a. Write a trigonometric model representing the situation.

b. At what time on that Labor Day does the first low tide occur?

c. What was the approximate depth of the water at 4:00 a.m. and at 9:00 p.m.?

d. What is the first time on that Labor Day that the water is 9 ft deep?

1. A Ferris Wheel 250 ft in diameter makes one revolution every 420 sec. The center of the wheel is 150 feet above the ground.

a. Write a trigonometric model representing the situation.

b. Using your equation, calculate how long after reaching the low point is a rider 120 ft above ground?

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