Download HAAChpt14PracticeTest

Honors Advanced Algebra with Trigonometry
Name:_______________________
Chapter 14
Date:________________________
Practice Test
Period:______________________
**NO CALCULATORS!!!**
Cosine of sum or difference
cos (A + B) = cos A cos B - sin A sin B
cos (A - B) = cos A cos B + sin A sin B
Double-Angle Identities
cos 2A = cos2 A - sin2 A
cos 2A = 1 - 2 sin2 A
Sine of sum or difference
sin (A + B) = sin A cos B + cos A sin B
sin (A - B) = sin A cos B - cos A sin B
cos 2A = 2 cos2 A - 1
sin 2A = 2 sin A cos A
1. Write the fundamental identities that you have memorized below (three reciprocal identities, two
quotient identities, three Pythagorean identities, and three negative angle identities).
Simplify the following to a single trig function, a power of a single trig function, or a constant.
2. 1 - cos2 x
3. sin (x - 90°)
2.
3.
4. csc2 x - 1
5. cot2 x - csc2 x
4.
5.
6.
cot x
csc x
7.
sec x csc x
tan x
6.
7.
8. 1 -
sin x
csc x
9. tan x - sec x csc x
8.
9.
Prove that each equation is an identity.
10.
tan x
= sec x csc x
1 − cos 2 x
12. 2 tan x csc 2x - tan2 x = 1
11. csc A sin 2A - sec A = cos 2A sec A
13.
1 + cos 2x
= cot x
sin 2x
Use the sum and/or difference identities to find the exact value of the following.
⎛ 7π ⎞
14. sin⎜ ⎟
⎝ 12 ⎠
15. cos255°
14.
15.
Solve each equation for solutions in the interval [0, 2π) by first solving for the trig function.
16. 2 sin x + 1 = 0
17. 2 cos 2 x + cos x − 1 = 0
16.
17.
18. cos 2 x =
3
4
18.
Solve each equation for solutions in the interval [0, 360°) by first solving for the trig function.
19. tan 2 x = 1
20. sin x + sin 2x = 0
19.
20.
21. cos
⎛ x⎞
2
=
⎝ 2⎠
2
21.