Download Trigonometry Review

AP Calculus AB
Trigonometry Review
In Exercises 1 & 2, list one positive and one negative coterminal angle.
1. 280ᵒ
2.
11𝜋
4
In Exercises 3 & 4, find the reference angle.
3.23210ᵒ
4.
7𝜋
6
In Exercises 5 & 6, solve for the missing variable.
5.
6.
In Exercises 7 & 8, find the exact values of the six trigonometric functions of the angle θ (in
standard position) whose terminal side passes through the point.
7. (3, -4)
2
5
8. (3 , 2)
In Exercises 9 – 11, sketch the graph of the function.
9. y = 2 + sin x
10. g(t) = 3 cos(t + π)
𝜋
11. f(t) = tan(t - 4 )
In Exercises 12 – 15, use the fundamental trigonometric identities to simplify the trigonometric
expression.
12. 𝑐𝑜𝑠 2 𝑥 + 𝑐𝑜𝑠 2 𝑥𝑐𝑜𝑡 2 𝑥
14.
1
1
− csc 𝜃−1
csc 𝜃+1
13. (sec 𝑥 − tan 𝑥)2
15.
𝑐𝑜𝑠2 𝑥
1−sin 𝑥
In Exercises 16 & 17, verify the trigonometric identity.
16.
1
tan 𝑥 csc 𝑥
= cos 𝑥
17. 𝑐𝑜𝑠 3 𝑥 𝑠𝑖𝑛2 𝑥 = (𝑠𝑖𝑛2 𝑥 − 𝑠𝑖𝑛4 𝑥) cos 𝑥
In Exercises 18 – 21, solve the trigonometric equation.
1
18. sin 𝑥 = √3 − sin 𝑥
19.
20. 𝑠𝑖𝑛2 𝑥 + 2 cos 𝑥 = 2
21. 2 sin 2𝑥 − √2 = 0
2
sec 𝑥 − 1 = 0
In Exercises 22 - 23, use the Law of Sines, Law of Cosines, and the given information to solve the
triangle.
22. A = 36ᵒ, a = 8, b = 5
23. a = 11, b = 14, c = 20