Download review for trig test

Review for Trigonometry Test
Name: __________________________________________
Due Date: ________
SECTION 1: TRIG REVIEW
Evaluate.
⎛
sin ⎜ −
1.
⎝
⎛
8π ⎞
3 ⎟⎠
2.
cos ⎜ −
3π ⎞
4 ⎟⎠
5.
sec ⎜ −
csc ⎜ −
4.
⎝
⎛
⎝
⎛
⎝
7π ⎞
3 ⎟⎠
π⎞
2 ⎟⎠
tan −π
6.
cot ⎜ −
Find the exact value of the remaining trig functions if:
5.
P = (–4, –1)
4
6.
cos θ =
6
sin
θ = ______
cos
tan
θ = ______
θ = ______
csc
sec
cot
θ = ______
θ = ______
θ = ______
sin
( )
3.
⎛
⎝
and
17π ⎞
6 ⎟⎠
tan θ < 0.
θ = ______
cot
θ = ______
sec
θ = ______
csc
θ = ______
tan
θ = ______
SECTION 2: INVERSES
1.
4.
7.
10.
13.
15.
2.
3.
5.
6.
8.
11.
9.
⎛
⎛ 3⎞⎞
sin ⎜ sin −1 ⎜ ⎟ ⎟
⎝ 2⎠⎠
⎝
14.
16.
12.
⎛
⎛ 3⎞⎞
tan ⎜ tan −1 ⎜ ⎟ ⎟
⎝ 2⎠⎠
⎝
SECTION 3: FORMULAS
Match the following sum and difference formulas.
List the double angle formulas
sin(2θ ) =
_____1.
A.
_____2.
B.
_____3.
C.
_____4.
D.
_____5.
E.
_____6.
F.
7.
sin165 
9.
cos ⎜
π⎞
⎟
⎝ 12 ⎠
⎛
cos(2θ ) =
cos(2θ ) =
cos(2θ ) =
8.
cos135 ! cos90 ! – sin135 ! sin90
10.
tan ⎜
⎛ 5π ⎞
⎟
⎝ 12 ⎠
!
11.
⎛ 5π ⎞
⎛ 5π ⎞
⎛π ⎞
π⎞
cos ⎜ ⎟ + sin ⎜ ⎟ cos ⎜ ⎟
⎟
⎝ 12 ⎠
⎝ 12 ⎠
⎝ 12 ⎠
⎝ 12 ⎠
⎛
sin ⎜
21 π
≤ a ≤π
53 2
Given that: cos
cosaa==− ,
Quadrant: __________
and
12.
5π
2π
− tan
6
3
5π
2π
1+ tan tan
6
3
tan
tan b =
5
3π
.
, π ≤b≤
12
2
Quadrant: __________
Find the exact values of the following:
13.
cos(a – b)
14.
sin(a + b)
15.
16.
cos(2a)
sin(2a)
SECTION 4: IDENTITIES
Write the three Pythagorean identities in the blanks below.
1. ______________________
2. ______________________
3. ______________________
Match each identity.
_____4.
A.
B.
_____5.
_____6.
C.
D.
E.
F.
G.
_____7.
_____8.
_____9.
10.
(1− sin x )(1+ tan x ) = 1
2
2
11.
sec2 x
= secx cscx
tan x
12.
1− tan 2 x
= 1− 2sin 2 x
1+ tan 2 x
13.
cosx + sin x tan x = secx
14.
(1+ tanθ )
15.
sin 2 x − sin 4 x = cos2 x − cos4 x
16.
sinθ + cosθ
= secθ + cscθ
sinθ cosθ
17.
secθ + tanθ
= sinθ sec2 θ
cosθ + cotθ
2
= sec2 θ + 2tanθ
SECTION 5: SOLVING EQUATIONS
Solve each equation and find the solutions on the interval [0,2 π )
2.
tanθ = 2sinθ
1.
2sinθ + 3 = 0
3.
⎛
⎞
(cotθ +1) ⎜⎝ cscθ − 12 ⎟⎠ = 0
4.
cos ( 2θ ) =
1
2
5.
⎛
sin ⎜ 3x +
⎝
π⎞
=1
18 ⎟⎠
6.
sin ( 2θ )sinθ = cosθ
Solve the equation and write the solutions in GENERAL FORM =)
1
8.
2cos2 θ − 5cosθ = −2
7.
tan 2 θ =
3