CPPC Practice Problems 1/11/16 Find the requested values. −4
& sin α < 0, find cosα & cscα . 1. If cot α =
3
⎛
π⎞
3. If cosθ = .54 find sin ⎜ θ − ⎟ 2⎠
⎝
3
5. If sinθ = find: 5
( )
a.sin −θ
( )
b. tan −θ
2. If secα = −4 & cscα > 0, find cosα & tan α . ⎛
π⎞
4. If cot θ = .54 find tan ⎜ θ − ⎟ 2⎠
⎝
⎛π
⎞
c. sin ⎜ − θ ⎟
⎝2 ⎠
⎛π
⎞
d. tan ⎜ − θ ⎟ ⎝2 ⎠
Simplify each expression. 2
2
2
6.
sin
x
cos
x
−
cos
x
7. (sin x + cos x)2 +(sin x − cos x)2 8. sin x + 2sin x cos x + cos x
4
2
2
4
−cot 2 x
9.
cos x + cot x Verify each identity. (
)
10. cos x sin x = sin x − sin x cos x
!
3
4
4
6
sin2 x + cos2 x
11.
= 1 2
2
cos x sec x
tan2 β
1− cos β
12.
=
cos β
1+ sec β
(
)(
13.
)
14. sec2 θ −1 sin2 θ −1 = −sin2 θ
1
1
+
= 2csc2 β
1− cos β 1+ cos β
15. csc x − sin x = cot x cos x