Download 7.4 - Double-Angle and Half

HAAT - Mr. Hayes
7.4 - Double-Angle and Half-Angle Identities
Retake Review
Name: ___________________________________
Date: ______________________
As always, please show work when appropriate. See Mr. Hayes and your book if you need help.
3.0 Questions
5.0 Questions
Use identities to find the indicated value for each angle
measure.
2 6
, tan θ < 0
Find sin(2θ).
11) sin θ = 7
Use identities to find the indicated value for each angle
measure.
24
1) cos θ = , sin θ < 0
Find sin(2θ).
25
2) sin θ = 12
, cos θ > 0
13
3) tan θ = 12
3π
, π < θ < 5
2
4 3π
4) sin θ = - , < θ < 2π
2
5
Find cos(2θ).
12) cos θ = Find sin(2θ).
13) sin θ = 20
, sin θ < 0
29
Find sin(2θ).
4 3
, tan θ < 0
7
Find sin(2θ).
1
14) cos 2θ = and θ terminates in quadrant I
3
Find cos(2θ).
Find sin θ.
3
5) cos 2θ = and θ terminates in quadrant III
5
π
4
15) cos 2θ = - and < θ < π
2
7
Find cos θ.
4
6) cos 2θ = and θ terminates in quadrant III
5
Find sin θ.
Determine all solutions of the equation in radians.
θ
1
16) Find cos , given that sin θ = and θ
2
4
Find cos θ.
terminates in 0 < θ < 90°.
Find the exact value by using a half-angle identity.
7) sin 75°
x
17) Find cos , given that sec x = 4 and x
2
8) cos 22.5°
π
terminates in 0 < x < .
2
Determine all solutions of the equation in radians.
θ
3
9) Find sin , given that sin θ = - and θ
2
5
x
18) Find tan , given that tan x = 3 and x
2
terminates in 270° < θ < 360°.
terminates in π < x < 3
θ
10) Find cos , given that cos θ = - and θ
5
2
terminates in 90° < θ < 180°.
1
3π
.
2
Answer Key
Testname: 7.4
1) - 336
625
2) - 119
169
3)
120
169
4) - 7
25
5) cos θ = - 2 5
5
6) cos θ = - 3 10
10
7)
1
2 + 3
2
8)
1
2 + 2
2
9)
10
10
10)
5
5
11)
-20 6
49
12) - 13)
840
841
-8 3
49
14) sin θ = 15) sin θ = 3
3
154
14
16)
8 + 2 15
4
17)
10
4
18)
10 + 1
-3
2