Download Ch. 5 Review

Honors Pre-Calculus
Ch. 5 Review
Name ___________________
Find the following trig identities:
1
1. If cos θ = 4 and 0˚ < θ < 90˚, find tan , cot θ, sin θ, and sec θ.
3
2. If cot x = – 2 and sec x < 0, find sin x and cos x.
Simplify each expression.
cot 𝐴
3. cos x + sin x tan x
4. tan 𝐴
5. sin2 θ cos2 θ – cos 2 θ
6.
csc2 𝑥 − cot2 𝑥
sin (−𝑥) cot 𝑥
Verify the following equations
7. cos x sec 2 x tan x – cos x tan3 x = sin x
9. 2-cos2x = 1 + sin2x
1+𝑡𝑎𝑛2 𝑥
8. csc 𝑥 sec 𝑥 = tan 𝑥
Find all solutions on the interval [0, 2)
11. 2sin2x + sinx – 1 = 0
10. 2sinx cos x = √3sinx
12. 2tan4x – tan2x – 15 = 0
Find all solutions on the interval [0,2)
13. sin2x –sin x +1 = cos2x
14. 2sin2x = cosx + 1
Find all solutions on the interval [0,2)
16. 1 + cosx = √3sinx
15. sinx - cosx = 1
Find the exact value of each trigonometric expression.
17. cos
5𝜋
12
20. tan (−
18. sin (–165°)
7𝜋
)
12
19. tan 345°
Simplify each expression.
21. cos
3𝜋
2
cos π – sin
3𝜋
2
sin π
tan 30° − tan 𝑥
22. 1 + tan 30° tan 𝑥
Write each trigonometric expression as an algebraic expression.
23. sin (arccos x + arcsin x)
24. cos (arccos
1
2
− arcsin 𝑥)
Verify each cofunction or reduction identity.
25. sin (360° + θ) = sin θ
26. cos (180° – θ) = –cos θ
Find the solutions to each expression on the interval [0, 2π).
5π
5π
27. cos ( 4 + 𝑥) + sin ( 4 − 𝑥) = 0