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Math 2412
Review Test 2
Name___________________________________
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Verify the identity
1) sec x -
2)
1
= sin x tan x
sec x
sin x - cos x cos x - sin x
+
= 2 - cscx sec x
sin x
cos x
3) 1 -
cos2 x
= sin x
1 + sin x
Find the exact value by using a sum or difference identity.
4) sin 15°
Find the exact value of the expression.
5) sin 255° cos 15° - cos 255° sin 15°
Use the given information to find the exact value of the expression.
4
12
6) Find cos (α + β).
sin α = , α lies in quadrant I, and cos β =
, β lies in quadrant I.
5
13
7) Find cos (α - β).
sin α =
7
2
, α lies in quadrant II, and cos β = , β lies in quadrant I.
25
5
Find the exact value by using a difference identity.
π
8) tan
12
Find the exact value under the given conditions.
3
π
20
π
9) sin α = , 0 < α < ; cos β =
, 0<β<
5
2
29
2
Find tan (α + β).
Use the figure to find the exact value of the trigonometric function.
10)
5
3
4
Find sin 2θ.
1
Use the given information to find the exact value of the expression.
4
11) Find tan 2θ. sin θ = , θ lies in quadrant II.
5
Rewrite the expression as an equivalent expression that does not contain powers of trigonometric functions greater than
1.
12) 8 cos2 x
Use a half-angle formula to find the exact value of the expression.
5π
13) sin
12
14) cos
3π
8
Use the given information given to find the exact value of the trigonometric function.
θ
15) sec θ = 4,
θ lies in quadrant I
Find cos .
2
Express the product as a sum or difference.
16) cos 4x cos 3x
17) sin 2x sin 5x
Solve the problem.
18) cos 3x - cos 5x
19) sin
9x
5x
+ sin
2
2
Find all solutions of the equation.
20) tan x sec x = -2 tan x
Solve the equation on the interval [0, 2π).
2
21) cos 2x =
2
22) sec2 x - 2 = tan2 x
23) 2 cos2 x + sin x - 2 = 0
Use a calculator to solve the equation on the interval [0, 2π). Round to the nearest hundredth.
24) cos 2x - cos x = 0
2
Answer Key
Testname: MATH 2412 T2RF08
1)
2)
3)
4)
2( 3 - 1)
4
5) -
3
2
6)
16
65
7)
-48 + 7 21
125
8) 2 - 3
144
9)
17
10)
24
25
11)
24
7
12) 4 + 4 cos 2x
1
13)
2+ 3
2
14)
15)
1
2
2-
2
10
4
16)
1
(cos x + cos 7x)
2
17)
1
(cos 3x - cos 7x)
2
18) 2 sin 4x sin x
7x
19) 2 sin
cos x
2
20) x =
21)
2π
4π
π
+ 2nπ or x =
+ 2nπ or
+ nπ
3
3
2
π 7π 9π 15π
,
,
,
8 8
8
8
22) no solution
π 5π
23) 0, π, ,
6 6
24) 0, 2.09, 4.19
3