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Trigonometry
Review 7.1-7.4
1. If sin  =
Name________________________________
2
, 90° < 𝜃 < 180°, find sec  .
5
2. If cot  =
5
, find tan  .
8
Express each value as a trigonometric function of an angle in Quadrant I.
3. tan
13𝜋
4. sin 875º
3
Simplify each expression.
5.
sec2 𝑥−1
6.
sec2 𝑥
tan  cot
tan 
Find a numerical value of one trig function of each x.
7.
1+tan2 𝑥
sec 𝑥
1
= sin2 𝑥 + sec2𝑥
8. (sin  )( sec  ) =
2
2
Verify each identity.
2
9. tan 2𝜃 = cot 𝜃−tan 𝜃
10. 1 +
1
2
sin 2𝐴 =
sec𝐴+sin 𝐴
sec 𝐴
11. cos (90 -  ) = sin 
12. tan(𝑥 + 45°) =
1+tan 𝑥
1−tan 𝑥
Use sum or difference identities to find the exact value of each trigonometric function.
13. sin 255
15. Find exact value of tan (x – y) if sin x = 
14. cos
7
12
5
4
and cos y =
and x and y are angles in quad IV.
5
13
16. If sec 𝜃 = 4 and 180° < 𝜃 < 270°, then find the exact value of cos 2𝜃, sin 2𝜃, and tan 2𝜃.
Use a half-angle identity to find the exact value of each trigonometric function.
17. tan 112.5
18. sin
5𝜋
8