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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