Free Printable Chapter 7 Review

1.

sin^-1(-1/2)

a)

π/3

b)

π/6

c)

5π/6

d)

-π/6

2.

tan(sin^-1(-1/2))

a)

√3

b)

√3/3

c)

-√3

d)

-√3/3

3.

cos^-1(√(3)/2)

a)

π/3

b)

2π/3

c)

π/6

d)

5π/6

4.

csc(cos^-1(√(3)/2))

a)

2

b)

-2

c)

2√3/3

d)

-2√3/3

5.

sec^-1(-2)

a)

π/3

b)

2π/3

c)

π/6

d)

5π/6

6.

tan^-1(√(3))

a)

π/3

b)

2π/3

c)

π/6

d)

5π/6

7.

csc^-1(-√(2))

a)

π/4

b)

3π/4

c)

-π/4

d)

-3π/4

8.

cos^-1(tan(-π/4))

a)

0

b)

π

c)

π/4

d)

3π/4

9.

sin^-1(-1) =

a)

π/2

b)

0

c)

-1

d)

-π/2

10.

cos^-1(0) =

a)

π/2

b)

π

c)

1

d)

none of these

11.

sin(cos^-1(0))=

a)

0

b)

1

c)

π/2

d)

π

12.

sin^-1(√(2)/2) =

a)

π/4

b)

π/3

c)

π/2

d)

π

13.

tan(cos^-1(-1))=

a)

undefined

b)

0

c)

½

d)

1

14.

tan(sin^-1(-1/2))=

a)

√(3)

b)

√(3)/3

c)

-√(3)

d)

-√(3)/3

15.

cos^-1(- √(3)/2) =

a)

π/3

b)

2π/3

c)

π/6

d)

5π/6

16.

tan^-1(-√(3))=

a)

π

b)

-π/6

c)

-π/3

d)

-π/4

17.

What range of angles for inverse cosine?

a)

[0, π]

b)

[0, 2π]

c)

[-π/2, π/2]

d)

[π/2, 3π/2]

18.

What is the range of angles for inverse sine?

a)

[0, π]

b)

[0, 2π]

c)

[-π/2, π/2]

d)

[π/2, 3π/2]

19.

What is the range of angles for inverse tangent?

a)

(0, π/2)

b)

(-π/2, π/2)

c)

(0, π)

d)

(0, 2π)

20.

Identify the single function value for: $\cos^{-1}\left(-\frac{\sqrt{3}}{2}\right).$

a)

5π/6

b)

2π/3

c)

-π/6

d)

7π/6

21.

Identify the single function value for: $\sin^{-1}\left(\frac{\sqrt{3}}{2}\right)$ .

a)

-π/3

b)

2π/3

c)

-2π/3

d)

π/3

22.

Identify the single function value for: $\cos^{-1}\left(0\right).$

a)

0

b)

$\frac{\pi}{2}$

c)

$\pi$

d)

$-\frac{\pi}{2}$

23.

Since $\left(\pi,-1\right)$ is a point on $f\left(x\right)=\cos x$ , which point will be found on $f^{-1}\left(x\right)=\cos^{-1}x$ ?

a)

$\left(\pi,1\right)$

b)

$\left(-\pi,1\right)$

c)

$\left(-1,\pi\right)$

d)

$\left(1,-\pi\right)$

24.

Identify the single function value for: $\tan^{-1}\left(\sqrt{3}\right).$

a)

$\frac{\pi}{6}$

b)

$\frac{\pi}{3}$

c)

$\frac{2\pi}{3}$

d)

$\frac{4\pi}{3}$

25.

What range of the inverse cosine function?

a)

[0, π]

b)

[0, 2π]

c)

[-π/2, π/2]

d)

[π/2, 3π/2]

26.

What is the range of the inverse sine function?

a)

[0, π]

b)

[0, 2π]

c)

[-π/2, π/2]

d)

[π/2, 3π/2]

27.

What is the range of the inverse tangent function?

a)

(0, π/2)

b)

(-π/2, π/2)

c)

(0, π)

d)

(0, 2π)

28.

Evaluate $\tan\left(Cos^{-1}\left(-\frac{3}{5}\right)\right)=$

a)

$-\frac{3}{5}$

b)

$\frac{3}{5}$

c)

$-\frac{4}{3}$

d)

$\frac{4}{3}$

e)

UNDEFINED

29.

Evaluate $\sin\left(Tan^{-1}\left(-\frac{4}{3}\right)\right)=$

a)

$-\frac{4}{5}$

b)

$\frac{4}{5}$

c)

$-\frac{3}{4}$

d)

$\frac{3}{4}$

e)

UNDEFINED

30.

arctan[tan( $\frac{5\pi}{4}$ )]

a)

$-\frac{\pi}{4}$

b)

$\frac{\pi}{4}$

c)

$\frac{5\pi}{4}$

d)

$\frac{3\pi}{4}$

31.

$\$ $Evaluate:\ \sec\left(\arcsin\left(\frac{2}{7}\right)\right)$

a)

$\frac{3\sqrt{5}}{7}$

b)

$\frac{\sqrt{45}}{7}$

c)

$\frac{7\sqrt{5}}{15}$

d)

$\frac{3\sqrt{5}}{2}$

32.

Given the Cos(x) = -2/3, then the Sec(x) = ?

a)

-2/3

b)

-3/2

c)

3/2

d)

2/3

33.

Sec(π/3) = ?

a)

1/2

b)

√(3)/2

c)

2

d)

√3

34.

Cot(7π/4) = ?

a)

-1

b)

1

c)

-√2

d)

√2

35.

Evaluate: Cot^-1(√3/3)

a)

π/3

b)

2π/3

c)

π/6

d)

5π/6

36.

Which of these has the same value as cot^-1(3)?

a)

tan (3)

b)

cot (⅓)

c)

tan^-1(⅓)

d)

3 tan^-1(⅓)

37.

Solve
cos²θ = ½
on θ∈[0, 2π)

a)

θ = π /4, 7π /4

b)

θ = π /4, 3π /4

c)

θ = 3π /4, 5π /4

d)

θ = π /4, 3π /4, 5π /4, 7π /4

38.

Solve
cos θ = -1
on θ∈[0, 2π)

a)

θ = π /2, 3π /2

b)

θ = π /2

c)

θ = 3π /2

d)

θ = π

39.

2 sinθ+3=2

a)

π/6,2π/3

b)

7π/6

c)

7π/6, 11π/6

40.

Solve on the domain [0, 2π)
1/2sec x - 1 = 0

a)

π/6, 5π/6

b)

π/3, 5π/3

c)

2π/3, 4π/3

d)

7π/6, 11π/6

41.

Solve on the domain [0, 2π)
4sin²x = 3

a)

π/6, 11π/6

b)

π/3, 2π/3

c)

π/6, 5π/6, 7π/6, 11π/6

d)

π/3, 2π/3, 4π/3, 5π/3

42.

Solve on the domain [0, 2π)
2sin x cos x = √2 cos x

a)

π/2, 3π/2

b)

0, π/4, 3π/4

c)

π/2, 3π/2, π/4, 3π/4

d)

No solution

43.

Solve on the domain [0, 2π)
cos² x + sin x + 1 = 0

a)

π

b)

3π/2

c)

π/6, 5π/6, 3π/2

d)

No solution

44.

Solve equation for $0\le\theta<2\pi$ .
$-1-2\sec^2\theta=-3\sec^2\theta$

a)

$\theta=0,\pi,\frac{4\pi}{3}$

b)

$\theta=0$

c)

$\theta=\frac{\pi}{4},\frac{3\pi}{4},\frac{5\pi}{4},\frac{7\pi}{4}$

d)

$\theta=0,\pi$

45.

Solve equation for $0\le\theta<2\pi$ .
$2\sqrt{3}\sec\theta\cos\theta=-3\sec\theta$

a)

$\theta=\frac{5\pi}{6}$

b)

$\theta=\frac{5\pi}{6},\frac{7\pi}{6}$

c)

$\theta=\frac{7\pi}{6},\frac{4\pi}{3}$

d)

$\theta=\frac{5\pi}{6},\frac{11\pi}{6}$

46.

Solve equation for $0\le\theta<2\pi$ .
$-\sin^2\theta=\sin\theta+1-3\sin^2\theta$

a)

$\theta=\frac{\pi}{2},\frac{11\pi}{6}$

b)

$\theta=\frac{\pi}{2},\frac{7\pi}{6},\frac{11\pi}{6}$

c)

$\theta=\frac{2\pi}{3},\frac{7\pi}{6}$

d)

$\theta=0,\frac{2\pi}{3},\frac{4\pi}{3}$

47.

Solve the following for cos²θ:
sin²θ + cos²θ = 1

a)

cos²θ = 1 - sin²θ

b)

cosθ = 1 + sin²θ

c)

cosθ = 1 - sinθ

d)

cos²θ = Adj/hyp

48.

Solve the following for tan²θ:
1 + tan²θ = sec²θ

a)

tan²θ = sec²θ + 1

b)

tan²θ = sec²θ - 1

c)

tanθ = secθ - 1

d)

tan²θ = opp/adj

49.

Rewrite tan(x) in terms of sin(x) and cos(x).

a)

tan(x) = cos(x)/sin(x)

b)

tan(x) = 1/cot(x)

c)

tan(x) = sin(x)/cos(x)

d)

tan(x) = opp/adj

50.

What is csc(x) equivalent to?

a)

1/sin(x)

b)

1/tan(x)

c)

sin(x)

d)

1/cos(x)

51.

Please select the correct solution

a)

csc² x

b)

cot² x

c)

sin² x

d)

sec² x

52.

Please select the correct solution cos²x + sin ²x=

a)

1

b)

csc²x + sec²x

c)

sin²x

d)

1 - sin²x

53.

Simplify

a)

sin²θ

b)

cosθ

c)

tanθ

d)

1- sin²θ

54.

Simplify

a)

-1

b)

sin θ

c)

csc θ

d)

1

55.

Simplify

a)

csc²θ

b)

sec²θ

c)

cscθ

d)

1

56.

sin²x + cos²x =

a)

1

b)

1/sinx

c)

sec²x

d)

csc²x

57.

1 - sin²x =

a)

cos²x

b)

cos²x+1

c)

csc²x

d)

tan²x

58.

tan²x + 1 =

a)

csc²x

b)

sec²x

c)

sec²x - 1

d)

cscx

59.

1 + cot²x =

a)

sec²x

b)

sec²x - 1

c)

tan²x

d)

csc²x

60.

1 - cos²x =

a)

sec²x

b)

csc²x

c)

sin²x

d)

sec²x - 1

61.

sec²x =

a)

sinx + cosx

b)

1 + csc²x

c)

1 + tan²x

d)

1 - sin²x

62.

csc²x - 1 =

a)

cot²x

b)

tan²x

c)

cot²x + 1

d)

sin²x + cos²x

63.

sec²x - 1 =

a)

cot²x

b)

csc²x

c)

1 + tan²x

d)

tan²x

64.

cos²x =

a)

1 - sec²x

b)

1 - sin²x

c)

sin²x

d)

1

65.

1/sinx

a)

tanx

b)

secx

c)

cscx

d)

cosx

66.

*

a)

csc² x

b)

sec² x

c)

cot² x

d)

tan² x

67.

a)

sin²θ

b)

cosθ

c)

tanθ

d)

1- sin²θ

68.

a)

-1

b)

sin θ

c)

csc θ

d)

1

69.

a)

csc²θ

b)

sec²θ

c)

cscθ

d)

1

70.

a)

secθ

b)

cos²θ

c)

sin²θ

d)

sin²θ/cos²θ

71.

a)

1/cos x

b)

1

c)

cot x

d)

-1

72.

a)

1/cos x

b)

1

c)

cot x

d)

-1

73.

Verify the following.
tanB (cotB + tanB) = sec²B

a)

1+ tan²B

b)

sec²B

c)

cot²B

d)

tan²B

74.

a)

(cos/sin)(sin/cos)

b)

cos

c)

sin

d)

(sin/cos)(cos/sin)

75.

Which of the following would be a step to prove the following identity?

a)

(1/ sin x) - (1 / cos x)

b)

(cos x - sin x) / ( sin x)

c)

(cos x - sin x) / (cos x)

d)

(1/ sin x cos x)

76.

a)

cot

b)

(1 / cos)

c)

tan

d)

(1 / sin)

77.

Verify the following:

a)

cos²x

b)

sin²x

c)

cot²x

d)

tan²x

78.

Which of the following is the same as $\cos\ \left(A+B\right)$

a)

$\sin A\cos\ B\ +\ \cos\ A\ \sin\ B$

b)

$\sin\ A\ \cos\ B\ -\ \cos\ A\ \sin\ B$

c)

$\cos\ A\ \cos\ B\ +\ \sin\ A\ \sin\ B$

d)

$\cos\ A\ \cos\ B\ -\ \sin\ A\ \sin\ B$

79.

Which of the following is equivalent to $\tan\ \left(A-B\right)$

a)

$\tan\ A\ -\ \tan\ B$

b)

$\frac{\tan\ A\ -\tan\ B}{1+\ \tan A\tan B}$

c)

$\frac{\tan\ A\ +\tan\ B}{1-\ \tan A\tan B}$

d)

$\frac{\sin\ A}{\cos\ B}$

80.

Expand $\sin\ \left(33^{o\ }+42^o\right)$

a)

$\sin\ 75^{o\ }$

b)

$\sin\ 33^o\cos42^o+\cos33^o\sin42^o$

c)

$\sin\ 33^o\cos42^o-\cos33^o\sin42^o$

d)

$\cos33^o\cos42^o+\sin33^o\sin42^o$

81.

Expand $\cos\ \left(\frac{\pi}{5}+\frac{\pi}{6}\right)$

a)

$\cos\frac{\pi}{5}\cos\frac{\pi}{6}-\sin\frac{\pi}{5}\sin\frac{\pi}{6}\$

b)

$\cos\frac{\pi}{5}\cos\frac{\pi}{6}+\sin\frac{\pi}{5}\sin\frac{\pi}{6}\$

c)

$\cos\ \frac{2\pi}{11}$

d)

$\cos\frac{\pi}{5}\sin\frac{\pi}{6}-\cos\frac{\pi}{5}\sin\frac{\pi}{6}\$

82.

$\cos75^o\cos15^o-\sin75^{o\ }\sin15^o$ is equivalent to

a)

$\sin\ 90^{o\ }$

b)

$\sin\ 60^{o\ }$

c)

$\cos\ 90^{o\ }$

d)

$\cos\ 60^{o\ }$

83.

$\frac{\tan45^o+\tan30^o}{1-\tan45^o\tan30^o}$ is equivalent to

a)

$\tan75^o$

b)

$\tan\ 15^o$

c)

$\frac{\sin45^o}{\cos30^o}$

d)

$\tan90^{o\ }$

84.

Use sum or difference angles identity to find the exact value for $\cos105^o$

a)

$\frac{\sqrt{6}+\sqrt{2}}{4}$

b)

$\frac{\sqrt{6}-\sqrt{2}}{4}$

c)

$\frac{-\sqrt{6}-\sqrt{2}}{4}$

d)

$\frac{\sqrt{2}-\sqrt{6}}{4}$

85.

Use sum or difference angles identity to find the exact value for $\sin\ \left(-15^o\right)$

a)

$\frac{\sqrt{6}+\sqrt{2}}{4}$

b)

$\frac{\sqrt{6}-\sqrt{2}}{4}$

c)

$\frac{\sqrt{2}-\sqrt{6}}{4}$

d)

$-\frac{\sqrt{3}}{2}$

86.

Given $\sin x=\frac{3}{5}and\ \sin y=\frac{2}{3},$ where $x\ and\ y$ are both in first quadrant. $Evaluate\ \sin\left(x+y\right)$

a)

$\frac{3\sqrt{5}+8}{15}$

b)

$\frac{4\sqrt{5}+6}{15}$

c)

$\frac{2\sqrt{5}+12}{15}$

d)

$\frac{4\sqrt{5}+2}{5}$

87.

Write the following expression as the sine, cosine, or tangent of an angle.
cos(175)cos(55)+sin(175)sin(55)

a)

sin(120)

b)

cos(120)

c)

cos(230)

d)

sin(230)

88.

sin 105º

a)

√3/2

b)

-1/4(√2 + √6)

c)

1/4 (√2 + √6)

d)

2-√3

89.

Find the exact value of the expression.
cos(20)cos(40) - sin(20)sin(40)

a)

1/4

b)

1/2

c)

√(3)/2

d)

√(3)

90.

Which of the following is NOT
a solution to
sin θ = √(3) / 2 ?

a)

π / 3

b)

2π / 3

c)

5π / 3

d)

7π / 3

91.

If $\sin A=\frac{3}{5},\sin B=\frac{2}{3},$ $and\ \angle A\ and\ \angle B$ are acute angles, what is the value of $\cos\left(A-B\right)?$

a)

$-\frac{2}{3}$

b)

$\frac{4\sqrt{5}-6}{15}$

c)

$\frac{4\sqrt{5}+2}{5}$

d)

$\frac{4\sqrt{5}+6}{15}$

92.

If $\cos A=\frac{1}{3}$ , then the positive value of $\tan\ \frac{A}{2}$ ?

a)

$\sqrt{2}$

b)

$\sqrt{3}$

c)

$\frac{\sqrt{3}}{3}$

d)

$\frac{\sqrt{2}}{2}$

93.

Expand and simplify $\tan\ \left(x+\frac{\pi}{4}\right)$

a)

$\tan\ x+1$

b)

$\tan x-1$

c)

$\frac{\tan\ x+1}{1-\tan x}$

d)

$\frac{\tan x-1}{1+\tan x}$

94.

Use sum or difference angles identity to find the exact value for $\cos105^o$

a)

$\frac{\sqrt{6}+\sqrt{2}}{4}$

b)

$\frac{\sqrt{6}-\sqrt{2}}{4}$

c)

$\frac{-\sqrt{6}-\sqrt{2}}{4}$

d)

$\frac{\sqrt{2}-\sqrt{6}}{4}$

95.

Use sum or difference angles identity to find the exact value for $\sin\ \left(-15^o\right)$

a)

$\frac{\sqrt{6}+\sqrt{2}}{4}$

b)

$\frac{\sqrt{6}-\sqrt{2}}{4}$

c)

$\frac{\sqrt{2}-\sqrt{6}}{4}$

d)

$-\frac{\sqrt{3}}{2}$

96.

Given $\sin x=\frac{3}{5}and\ \sin y=\frac{2}{3},$ where $x\ and\ y$ are both in first quadrant. $Evaluate\ \sin\left(x+y\right)$

a)

$\frac{3\sqrt{5}+8}{15}$

b)

$\frac{4\sqrt{5}+6}{15}$

c)

$\frac{2\sqrt{5}+12}{15}$

d)

$\frac{4\sqrt{5}+2}{5}$

97.

Given $\tan A=\frac{2}{3}and\ \tan B=\frac{1}{2},\$ where $\angle A\ and\ \angle B\ in\ quadrant\ I$ $Evaluate\ \tan\left(A+B\right)$

a)

$\frac{1}{8}$

b)

$\frac{7}{8}$

c)

$\frac{1}{4}$

d)

$\frac{7}{4}$

98.

Use a double-angle or half-angle identity to find the exact value of each expression

cos θ = 4/5 and 270° < θ < 360°Find sin 2θ

a)

-1/5

b)

24/25

c)

-24/25

d)

-25/24

99.

Use a double-angle or half-angle identity to find the exact value of each expression
sin θ = −3/5 and 3π/2 < θ < 2π Find tan θ/2

a)

-1/3

b)

-√3

c)

√3/3

d)

-1

100.

Use a double-angle identity to find the exact value of each expression
cos θ = 4/5 and 270° < θ < 360°
Find sin 2θ

a)

-1/5

b)

24/25

c)

-24/25

d)

-25/24

101.

Use a double-angle or half-angle identity to find the exact value of each expression
cos θ = 4/5 and 270° < θ < 360°Find sin 2θ

a)

-1/5

b)

24/25

c)

-24/25

d)

-25/24

102.

Use a double-angle or half-angle identity to find the exact value of each expression
sin θ = −3/5 and 3π/2 < θ < 2π Find tan θ/2

a)

-1/3

b)

-√3

c)

√3/3

d)

-1

103.

Find the exact value of sin 2x if sin x = 12/13 and x is in the first quadrant.

a)

120/169

b)

25/169

c)

60/169

d)

5/13

104.

Use the information about the angle θ, 0≤θ<2π to find the exact value of
sin (2θ)
1. sin θ= 3/5 , 0<θ<π/2

a)

24/7

b)

7/25

c)

24/25

d)

1/2

105.

sin2u =

a)

(sinu)(cosu)

b)

2(sinu)(cosu)

c)

(sinu)^2

d)

2(sinu)^2

106.

cos2u =

a)

2(sinu)(cosu)

b)

(cosu)^2 - (sinu)^2

c)

2(cosu)^2 - 2

d)

(sinu)^2 - (cosu)^2

107.

If cosx = - 4/5, find secx.

a)

-5/4

b)

-3/5

c)

5/3

d)

√3/2

108.

Find the exact value of sin 2x if sin x = 12/13 and x is in the first quadrant.

a)

120/169

b)

25/169

c)

60/169

d)

5/13

109.

Using the second identity, find Cos(50)

a)

sin²(25) - cos²(25)

b)

cos²(50) - sin²(50)

c)

cos²(25) - sin²(25)

d)

sin²(50) - cos²(50)

110.

Using the first identity, find Sin(180)

a)

2sin(90)cos(90)

b)

2sin(180)cos(180)

c)

sin(90)cos(90)

d)

sin(180)cos(180)

111.

Using the third identity, find Cos(40)

a)

2cos² (40) - 1

b)

2cos² (20) - 1

c)

2cos² (20) + 1

d)

2cos² (40) + 1

112.

Using the fourth identity, find Cos(120)

a)

1-2sin²(120)

b)

1+2sin²(120)

c)

1+2sin²(60)

d)

1-2sin²(60)

113.

Use a double-angle identity to find the exact value of each expression
cos θ = 4/5 and 270° < θ < 360°
Find sin 2θ

a)

-1/5

b)

24/25

c)

-24/25

d)

-25/24

114.

Use the Half-angle formulas to find the exact value of each expression
sin 22.5º

a)

√(2 + √3)/2

b)

√(2 - √2)/2

c)

√(2 + √2)/2

d)

√(2 - √3)/2

115.

Which identity represents a double-angle identity for sin 2θ?

a)

2sinθcosθ

b)

cos²θ - sin²θ

c)

1 - 2sin²θ

d)

2cos²θ - 1

116.

Use Sum or Difference Identities to find the exact value of each expression.

cos(75°)

a)

1/4

b)

c)

d)

117.

Use a half-angle identity to find the exact value of $\sin165\degree$

a)

$\frac{\sqrt{6}-\sqrt{2}}{4}$

b)

$-2-\sqrt{3}$

c)

$\frac{\sqrt{2-\sqrt{2}}}{2}$

d)

$-\frac{\sqrt{3}}{3}$

118.

Use a half-angle identity to find the exact value of $\tan\left(\frac{5\pi}{8}\right)$

a)

$-\sqrt{3+2\sqrt{2}}$

b)

$\frac{\sqrt{2-\sqrt{2}}}{2}$

c)

$-2$

d)

$\frac{\sqrt{3}}{3}$

119.

Use a half-angle identity to find the exact value of $\tan\left(\frac{5\pi}{8}\right)$

a)

$-\sqrt{3+2\sqrt{2}}$

b)

$\frac{\sqrt{2-\sqrt{2}}}{2}$

c)

$-2$

d)

$\frac{\sqrt{3}}{3}$

120.

Use a half-angle identity to find the exact value of $\cot\left(\frac{7\pi}{12}\right)$

a)

$-\frac{\sqrt{3}}{3}$

b)

$-\sqrt{3}$

c)

$\sqrt{4-2\sqrt{2}}$

d)

$-2+\sqrt{3}$

121.

Use a half-angle identity to find the exact value of $\sec67.5\degree$

a)

$0$

b)

$\sqrt{6}+\sqrt{2}$

c)

$\sqrt{4+2\sqrt{2}}$

d)

$1$

122.

$\tan\theta=-\sqrt{14}$ and $\frac{\pi}{2}<\theta<\pi$ find $\cos\left(\frac{\theta}{2}\right)$

a)

$\sqrt{26}$

b)

$\frac{\sqrt{58+10\sqrt{29}}}{2}$

c)

$\frac{\sqrt{450-30\sqrt{15}}}{30}$

d)

$\frac{\sqrt{105-7\sqrt{15}}}{7}$

123.

$\tan\theta=-2$ and $90\degree<\theta<180\degree$ find $\csc\left(\frac{\theta}{2}\right)$

a)

$\frac{\sqrt{50+10\sqrt{5}}}{10}$

b)

$\frac{\sqrt{10-2\sqrt{5}}}{2}$

c)

$\frac{\sqrt{50-10\sqrt{5}}}{10}$

d)

$\frac{\sqrt{5}}{5}$

124.

$\tan\theta=-2$ and $90\degree<\theta<180\degree$ find $\csc\left(\frac{\theta}{2}\right)$

a)

$\frac{\sqrt{50+10\sqrt{5}}}{10}$

b)

$\frac{\sqrt{10-2\sqrt{5}}}{2}$

c)

$\frac{\sqrt{50-10\sqrt{5}}}{10}$

d)

$\frac{\sqrt{5}}{5}$

125.

$\ simplify\ \frac{\sin\theta\ \csc\theta}{\cot\theta}$

a)

$\cot\theta$

b)

$\cos\theta$

c)

$\sin\theta$

d)

$\tan\theta$

126.

$\tan^2\theta\left(\cot^2\theta-\cos^2\theta\right)$ simplify

a)

$\cot\theta^2$

b)

$\cos\theta^2$

c)

$\tan\theta^2$

d)

$\sin\theta^2$

127.

$\frac{\tan^2\theta+1}{\tan^2\theta}$

a)

$\csc^2\theta$

b)

$\tan^2\theta$

c)

$\cos^2\theta$

d)

$\sin^2\theta$

128.

$\cos\ \frac{7\pi}{12}$

a)

$\frac{\sqrt{2}}{2}$

b)

$\frac{\pm\sqrt{6}+\sqrt{2}}{4}$

c)

$-\frac{\sqrt{2}}{2}$

d)

$\frac{-\sqrt{6}+\sqrt{2}}{4}$

129.

$find\ \ \ \ \tan2\theta\ \ \ \ \ \ if\ \cos\theta=-\frac{1}{3}\ \ and\ 90<\theta<180$

a)

$\frac{4\sqrt{2}}{7}$

b)

$-\frac{2\sqrt{4}}{7}$

c)

$\frac{4\sqrt{7}}{2}$

d)

$\frac{-4\sqrt{2}}{7}$

130.

$solve\ \ \sin^2\theta+2\cos^2\theta=4$

a)

90,210,330

b)

180,90,270

c)

NO solution

d)

$\frac{7\pi}{6},\frac{11\pi}{6}$

131.

$\sin\theta\cos\theta-\frac{1}{2}\cos\theta\ =0\ \ \ \ \ solve\ it$

a)

$\theta=90$

b)

$\theta=30$

c)

$\theta=150$

d)

$\theta=90,30,150$

132.

What is the range of $y=\sin^{-1}x$ ?

a)

$\left(-\infty,\infty\right)$

b)

$\left[-1,1\right]$

c)

$\left[0,2\pi\right]$

d)

$\left[-\frac{\pi}{2},\frac{\pi}{2}\right]$

133.

What is the domain of $y=\cos^{-1}x$ ?

a)

$\left(-\infty,\infty\right)$

b)

$\left[-1,1\right]$

c)

$\left[0,2\pi\right]$

d)

$\left[-\frac{\pi}{2},\frac{\pi}{2}\right]$

134.

Solve
cos θ = -1
on θ∈[0, 2π)

a)

θ = π /2, 3π /2

b)

θ = π /2

c)

θ = 3π /2

d)

θ = π

135.

Solve
cos²θ = ½
on θ∈[0, 2π)

a)

θ = π /4, 7π /4

b)

θ = π /4, 3π /4

c)

θ = 3π /4, 5π /4

d)

θ = π /4, 3π /4, 5π /4, 7π /4

136.

a)

A

b)

B

c)

C

d)

D

137.

2 sinθ+3=2

a)

π/6,2π/3

b)

7π/6

c)

7π/6, 11π/6

138.

Solve on the domain [0, 2π)
1/2sec x - 1 = 0

a)

π/6, 5π/6

b)

π/3, 5π/3

c)

2π/3, 4π/3

d)

7π/6, 11π/6

139.

Solve on the domain [0, 2π)
4sin²x = 3

a)

π/6, 11π/6

b)

π/3, 2π/3

c)

π/6, 5π/6, 7π/6, 11π/6

d)

π/3, 2π/3, 4π/3, 5π/3

140.

Solve on the domain [0, 2π)
2sin x cos x = √2 cos x

a)

π/2, 3π/2

b)

0, π/4, 3π/4

c)

π/2, 3π/2, π/4, 3π/4

d)

No solution

141.

Solve on the domain [0, 2π)
cos² x + sin x + 1 = 0

a)

π

b)

3π/2

c)

π/6, 5π/6, 3π/2

d)

No solution

142.

Solve equation for $0\le\theta<2\pi$ .
$-1-2\sec^2\theta=-3\sec^2\theta$

a)

$\theta=0,\pi,\frac{4\pi}{3}$

b)

$\theta=0$

c)

$\theta=\frac{\pi}{4},\frac{3\pi}{4},\frac{5\pi}{4},\frac{7\pi}{4}$

d)

$\theta=0,\pi$

143.

Solve equation for $0\le\theta<2\pi$ .
$2\sqrt{3}\sec\theta\cos\theta=-3\sec\theta$

a)

$\theta=\frac{5\pi}{6}$

b)

$\theta=\frac{5\pi}{6},\frac{7\pi}{6}$

c)

$\theta=\frac{7\pi}{6},\frac{4\pi}{3}$

d)

$\theta=\frac{5\pi}{6},\frac{11\pi}{6}$

144.

Solve equation for $0\le\theta<2\pi$ .
$-\sin^2\theta=\sin\theta+1-3\sin^2\theta$

a)

$\theta=\frac{\pi}{2},\frac{11\pi}{6}$

b)

$\theta=\frac{\pi}{2},\frac{7\pi}{6},\frac{11\pi}{6}$

c)

$\theta=\frac{2\pi}{3},\frac{7\pi}{6}$

d)

$\theta=0,\frac{2\pi}{3},\frac{4\pi}{3}$

145.

$\tan\ x\ +\ \sqrt{3}=0$

a)

$x\ =\ \frac{2\pi}{3}+\pi n$

b)

$x=\frac{2\pi}{3}+2\pi n$

c)

$x=\frac{\pi}{3}+\pi n$

d)

$x=\frac{\pi}{3}+2\pi n$

146.

$3\sin\ x\ +\ 1\ =\ \sin\ x$

a)

$x=\frac{7\pi}{6}+2\pi n,\ \ \ x\ =\ \frac{11\pi}{6}+2\pi n$

b)

$x=\frac{\pi}{6}+2\pi n,\ \ \ x\ =\ \frac{5\pi}{6}+2\pi n$

c)

$x=\frac{4\pi}{3}+2\pi n,\ \ \ \ x=\frac{5\pi}{3}+2\pi n$

d)

$x=\frac{\pi}{4}+\pi n$

147.

$\sin^2x=3\cos^2x$
(Hint: use a Pythagorean identity to get it all in terms of sine or cosine.)

a)

$x=\frac{\pi}{3}+\pi n,\ \ \ x=\frac{2\pi}{3}+\pi n$

b)

$x=\frac{\pi}{3}+2\pi n$

c)

$x=\frac{2\pi}{3}+2\pi n$

d)

$x=all\ real\ numbers$

148.

$\tan^2\ x=3$

a)

$x=\frac{\pi}{3}+\pi n,\ \ \ x=\frac{2\pi}{3}+\pi n$

b)

$x=\frac{\pi}{6}+\pi n,\ \ \ \ x=\frac{5\pi}{6}+\pi n$

c)

$x=\frac{\pi}{3}+2\pi n,\ \ \ \ x=\frac{2\pi}{3}+\pi n$

d)

No solution

149.

$\tan^2\ x=3$

a)

$x=\frac{\pi}{3}+\pi n,\ \ \ x=\frac{2\pi}{3}+\pi n$

b)

$x=\frac{\pi}{6}+\pi n,\ \ \ \ x=\frac{5\pi}{6}+\pi n$

c)

$x=\frac{\pi}{3}+2\pi n,\ \ \ \ x=\frac{2\pi}{3}+\pi n$

d)

No solution

150.

$2\sin x-1=0$

a)

$x=\frac{\pi}{6}+2\pi n,\ \ \ \ x=\frac{5\pi}{6}+2\pi n$

b)

$x=\frac{\pi}{3}+\pi n,\ \ \ \ \ x\ =\ \frac{2\pi}{3}+\pi n$

c)

$x=\frac{\pi}{6}+2\pi n,\ \ \ \ \ x=\frac{7\pi}{6}+2\pi n$

d)

No Solution

151.

$\cos x\sin x=2\cos x$

a)

$x=\frac{\pi}{2}+\pi n$

b)

$x=\pi n$

c)

$x=\frac{\pi}{4}+2\pi n$

d)

No Solution

152.

Solve for x:
$2\tan\left(\frac{x}{2}-π\right)=2$

a)

$\frac{3\pi}{5}$

b)

$\frac{8\pi}{9}$

c)

$\frac{5\pi}{2}$

d)

$\frac{9\pi}{2}$

153.

Solve equation for $0\le\theta<2\pi$ .
$1=5-8\cos\theta$

a)

$\theta=\frac{\pi}{6},\frac{\pi}{3},\frac{11\pi}{6}$

b)

$\theta=\frac{\pi}{6},\frac{11\pi}{6}$

c)

$\theta=\frac{\pi}{6}$

d)

$\theta=\frac{\pi}{3},\frac{5\pi}{3}$

154.

Solve for all values of x over the interval [0,2π]

a)

$\frac{\pi}{6}\ and\ \frac{7\pi}{6}$

b)

$\frac{5\pi}{6}\ and\ \frac{11\pi}{6}$

c)

$\frac{\pi}{3}\ and\ \frac{5\pi}{3}$

d)

$\frac{2\pi}{3}\ and\ \frac{4\pi}{3}$

155.

Solve equation for $0\le\theta<2\pi$ .
$\sec^2\theta+3=2\sec\theta+2$

a)

$\theta=0,\frac{\pi}{2},\frac{2\pi}{3},\frac{5\pi}{3}$

b)

$\theta=\frac{\pi}{3},\pi,\frac{5\pi}{3}$

c)

$\theta=\frac{\pi}{4}$

d)

$\theta=0$

156.

Solve equation for $0\le\theta<2\pi$ .
$3\sin^2\theta=7\sin^2\theta+4\sin\theta+1$

a)

$\theta=\frac{7\pi}{6}$

b)

$\theta=0,\frac{\pi}{3},\frac{5\pi}{3}$

c)

$\theta=\frac{3\pi}{4},\frac{7\pi}{4}$

d)

$\theta=\frac{7\pi}{6},\frac{11\pi}{6}$

157.

Solve for x:
$2\cos^2\left(x\right)+\cos\left(x\right)-1=0$
Check all possible answers

a)

x = 0

b)

x = $-\frac{\pi}{3}$

c)

x = $\pi$

d)

x = $\frac{\pi}{3}$

e)

x = $\frac{3\pi}{4}$

158.

Which identity represents a double-angle identity for sin 2θ?

a)

2sinθcosθ

b)

cos²θ - sin²θ

c)

1 - 2sin²θ

d)

2cos²θ - 1

159.

Which identity does not represent a double-angle identity for cos 2θ?

a)

2sinθcosθ

b)

cos²θ - sin²θ

c)

1 - 2sin²θ

d)

2cos²θ - 1

Chapter 7 Review

Total questions: 159

Worksheet time: 40hrs 45mins

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