Name:_________________________________Period:___ Date



Name:_________________________________Period:___ Date:_________

Review#9: Identities and Trig Equations

A. Calculator

Solve by graphing. Use a graphing calculator to solve each equation for [pic]. Draw a graph and express answers in terms of radians rounded to 3 decimal places.

1. 5cos2x = 3 2. [pic]

B. Non-Calculator

Solve each equation for [pic].

3. [pic] 4. [pic]

5. [pic] 6. [pic]

7. [pic] 8. 4sin2x = 1 + 4cosx

9. sin3x = -1 10. secx = tan x + cot x

Use trig identities to simplify each of the following expressions.

11. [pic] = __________ 12. csc2x – 1 = __________

13. [pic] = __________ 14. [pic]= __________

15. [pic] = __________ 16. [pic]= ___________

Verify each identity.

17. sinθ tanθ + cos θ = sec θ 18. [pic]

19. [pic] 20. [pic]

21. Write the exact value for each of the following trig functions.

a) [pic]= _______ f) [pic] = _______

b) [pic] = _______ g) [pic] = _______

c) [pic] = _______ h) [pic] = _______

d) [pic] = _______ i) [pic] = _______

e) [pic] = ______ j) [pic] = _______

Answers.

1. .464, 2.678, 3.605, 5.820

2. 2.209, 4.075

3. [pic]

4. [pic]

5. 0, (, 2(

6. [pic]

7. [pic]

8. [pic]

9. [pic]

10. No Solution

11. csc2x

12. cot2x

13. sec2x

14. [pic]

15. 1

16. -cosx

17. – 20. Proofs

21.

-----------------------

[pic]

[pic]

a) 1 f) -1

b) 0 g) [pic]

c) [pic] h) [pic]

d) [pic] i) -1

e) [pic] j) [pic]

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