Download Review for Exam 3

Math 2412 Review Items for Exam 3
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Prove the identity.
Use the given information to find the exact value of the
expression.
4
13) Find cos (α + β).
sin α = , α lies in
5
1
1) sec x = sin x tan x
sec x
2) sin2 x + sin2 x cot2 x = 1
quadrant I, and cos β =
Show that the equation is not an identity by finding a
value of x for which both sides are defined but not equal.
3) sin (x - π) = sin x
14) Find sin (α + β).
12
, β lies in quadrant I.
13
tan α =
quadrant III, and cos β = Identify α and β in the following expression which is the
right side of the formula for cos (α - β).
4) cos (170°) cos (50°) + sin (170°) sin (50°)
15
, α lies in
8
7
, β lies in
25
quadrant II.
Find the exact value by using a difference identity.
15) tan 105°
Write the expression as the cosine of an angle, knowing
that the expression is the right side of the formula for cos (
α - β) with particular values for α and β.
5) cos (155°) cos (35°) + sin (155°) sin (35°)
Use trigonometric identities to find the exact value.
tan 175° - tan 55°
16)
1 + tan 175° tan 55°
Find the exact value of the expression.
6) cos (245° - 5°)
Complete the identity.
17) tan (π - θ) = ?
Complete the identity.
11π
7) cos (x )=?
6
Find the exact value under the given conditions.
24
3π
20 π
18) tan α =
, π<α<
; cos β = ,
<β
7
2
29 2
< π Find tan (α + β).
Find the exact value by using a sum or difference identity.
8) sin (185° - 65°)
Use the figure to find the exact value of the trigonometric
function.
19)
9) sin 165°
Find the exact value of the expression.
10) sin 255° cos 15° - cos 255° sin 15°
13
5
11) cos 15° cos 45° - sin 15° sin 45°
12
Find cos 2θ.
Prove the identity.
sin (α + β)
12)
= tan α + tan β
cos α cos β
20)
25
7
24
Find cos 2θ.
1
Use the given information to find the exact value of the
expression.
20
21) Find sin 2θ. cos θ =
, θ lies in quadrant IV.
29
22) Find sin 2θ. cos θ =
33) cos 2x cos 4x
Solve the problem.
34) sin 8x - sin 2x
7
, θ lies in quadrant IV.
25
35) cos
Write the expression as the sine, cosine, or tangent of a
double angle. Then find the exact value of the expression.
23) cos2 105° - sin2 105°
5x
3x
+ cos
2
2
Complete the identity.
sin 3x + sin 5x
36)
=?
cos 2x + cos 4x
24) cos2 120° - sin2 120°
Find all solutions of the equation.
37) 2 cos x + 2 = 0
Complete the identity.
25) sin 2x - cot x = ?
Solve the equation on the interval [0, 2π).
3
38) cos 2x =
2
Rewrite the expression as an equivalent expression that
does not contain powers of trigonometric functions greater
than 1.
26) sin3 x
39) 2 sin 2 x = sin x
40) tan x + sec x = 1
27) 8 sin2 x cos2 x
41) sin2 x - cos2 x = 0
Use a half-angle formula to find the exact value of the
expression.
28) cos 112.5°
Solve the equation on the interval [0, 2π).
42) sin x - 2 sin x cos x = 0
Use a half-angle formula to find the exact value of the
expression.
3π
29) cos
8
Solve the equation on the interval [0, 2π).
43) tan 2x - tan x = 0
44) sin2 2x = 1
Use the given information given to find the exact value of
the trigonometric function.
30) sec θ = 4,
θ lies in quadrant I
Find cos
θ
.
2
Use a calculator to solve the equation on the interval [0, 2
π). Round the answer to two decimal places.
45) cos x = 0.60
Use a calculator to solve the equation on the interval [0, 2
π). Round to the nearest hundredth.
46) cos 2x - cos x = 0
Complete the identity.
θ
31) sin2 = ?
2
Express the product as a sum or difference.
32) sin 5x cos 2x
2
Answer Key
Testname: 2412REVIEW3SP2011
1) sin x tan x
2) 1
π
3)
2
29)
4) α = 170°, β = 50°
5) cos (120°)
1
6) 2
7)
30)
1
( 3 cos x - sin x)
2
3
2
8)
2( 3 - 1)
4
9)
10) -
1
2
22-
2
2
10
4
31)
csc θ - cot θ
2 csc θ
32)
1
(sin 7x + sin 3x)
2
33)
1
(cos 2x + cos 6x)
2
34) 2 sin 3x cos 5x
x
35) 2 cos 2x cos
2
3
2
36)
1
11)
2
sin 4x
cos 3x
37) x =
12) tan α + tan β
16
13)
65
14) -
1
2
28) -
38)
87
425
3π
5π
+ 2nπ or x =
+ 2nπ
4
4
π 11π 13π 23π
,
,
,
12 12 12 12
39) 0, π,
π 5π
,
6 6
15) -2 - 3
16) - 3
17) -tan θ
333
18)
644
40) 0
π 3π 5π 7π
41) ,
,
,
4 4
4 4
19)
119
169
20)
527
625
43) 0, π
π 3π 5π 7π
44) ,
,
,
4 4
4 4
42) 0,
45) 0.93, 5.36
46) 0, 2.09, 4.19
840
21) 841
22) -
336
625
23) -
3
2
24) -
π
5π
, π,
3
3
1
2
25) -cot x cos 2x
3
1
26) sin x - sin 3x
4
4
27) 2 sin 2x
3