Free Printable Unit 10 Test review

1.

Name the reference angles.

Select all that apply.

a)

30

b)

45

c)

60

d)

90

2.

Match the following radian measure to the correct degree measure

a)

$\frac{\pi}{6}$

1.

30

b)

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

2.

45

c)

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

3.

60

d)

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

4.

90

3.

Match the following trig functions to the correct trig values

a)

$\frac{\ 1}{2}$

1.

sin(30)

b)

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

2.

sin(45)

c)

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

3.

sin(60)

d)

0

4.

sin(90)

4.

Match the following trig functions to the correct trig values

a)

$\frac{\ 1}{2}$

1.

cos(60)

b)

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

2.

cos(45)

c)

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

3.

cos(30)

d)

0

4.

cos(90)

5.

Match the following trig functions to the correct trig values

a)

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

1.

tan(30)

b)

1

2.

tan(45)

c)

$\sqrt{\ 3}$

3.

tan(60)

d)

undefined

4.

tan(90)

6.

Determine the reference angle for:

$330\degree$

7.

Determine the reference angle for:

$120\degree$

8.

Determine the reference angle for:

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

9.

Determine the reference angle for:

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

10.

Determine the reference angle for:

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

11.

Find the exact value of:

$Cos\left(\frac{\ 7\pi}{4}\right)$

a)

-1/2

b)

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

c)

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

d)

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

12.

Find the exact value of:

$Tan\left(\frac{\ 4\pi}{3}\right)$

a)

-1

b)

$\sqrt{\ 3}$

c)

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

d)

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

13.

Find the exact value of:

$Sin\left(\frac{11\pi\ }{6}\right)$

a)

-1/2

b)

0

c)

1/2

d)

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

14.

What is the value of

$\sin\left(\frac{4\pi}{3}\right)$ ?

a)

$-\frac{1}{2}$

b)

$\frac{1}{2}$

c)

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

d)

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

15.

What is the value of

$\ \cos\left(\frac{4\pi}{3}\right)$ ?

a)

$-\frac{1}{2}$

b)

$\frac{1}{2}$

c)

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

d)

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

16.

What is the value of

$\ \tan\left(\frac{4\pi}{3}\right)$ ?

a)

$0$

b)

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

c)

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

d)

$-\ \sqrt{3}$

17.

What is the value of

$\ \sin\left(\frac{\pi}{6}\right)$ ?

a)

$-\frac{1}{2}$

b)

$\frac{1}{2}$

c)

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

d)

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

18.

What is the value of

$\ \cos\left(\frac{\pi}{6}\right)$ ?

a)

$-\frac{1}{2}$

b)

$\frac{1}{2}$

c)

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

d)

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

19.

Find the exact value of each trigonometric function:

\tan270\degree

a)

$0$

b)

Undefined

c)

$-1$

d)

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

20.

Find the exact value of each trigonometric function:

$\tan\frac{\ \pi}{2}$

a)

$0$

b)

Undefined

c)

$-1$

d)

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

21.

What is the reference angle for 125°?

a)

235°

b)

125°

c)

75°

d)

55°

22.

What is the reference angle for -30°?

a)

150°

b)

30°

c)

80°

d)

60°

23.

What is the reference angle for -310⁰?

a)

50⁰

b)

-50⁰

c)

20⁰

d)

40⁰

24.

What is the reference angle?

a)

163

b)

73

c)

27

d)

107

25.

What is the reference angle for 2pi/3

a)

pi/4

b)

7pi/6

c)

4pi/3

d)

pi/3

26.

Which of the following is a correct representation of the reference angle of $\theta=210\degree$

a)

b)

c)

d)

27.

Which of the following is a correct representation of the reference angle of $\theta=-150\degree$

a)

b)

c)

d)

28.

$\tan\ 300\degree$ = ______

a)

$\frac{1}{\sqrt{3}}\ or\ \frac{\sqrt{3}}{3}$

b)

$-\ \frac{1}{\sqrt{3}}\ or\ \ -\frac{\sqrt{3}}{3}$

c)

$\sqrt{3}$

d)

$-\sqrt{3}$

29.

If $\sin\theta\ =\frac{3}{5}$ and $\frac{\pi}{2}\le\theta\le\frac{3\pi}{2}$ , find $\cos\theta$

a)

$\frac{4}{5}$

b)

$-\frac{4}{5}$

c)

$\frac{3}{4}$

d)

$-\frac{3}{4}$

30.

\sin225\degree

=_______

a)

$\frac{1}{2}$

b)

$-\frac{1}{2}$

c)

$\frac{1}{\sqrt{2}}$

d)

$-\frac{1}{\sqrt{2}}$

31.

$\sin\ \frac{5\pi}{3}$ = _______

a)

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

b)

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

c)

$\frac{1}{2}$

d)

$-\frac{1}{2}$

32.

$\cos\ \frac{5\pi}{6}$ = _______

a)

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

b)

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

c)

$\frac{1}{2}$

d)

$-\frac{1}{2}$

33.

\cos315\degree

= ______

a)

$\frac{1}{2}$

b)

$-\frac{1}{2}$

c)

$\frac{1}{\sqrt{2}}$

d)

$-\frac{1}{\sqrt{2}}$

34.

$\tan\ \frac{7\pi}{6}$ = _____

a)

$\frac{1}{\sqrt{3}}$

b)

$-\frac{1}{\sqrt{3}}$

c)

$\sqrt{3}$

d)

$-\sqrt{3}$

35.

\sin90\degree

= ______

a)

0

b)

1

c)

-1

d)

does not exist

36.

a)

A

b)

B

c)

C

d)

D

37.

If θ is an angle in Quadrant I, which trig ratios will be positive

a)

sin θ

b)

cos θ

c)

tan θ

d)

All the above (sin θ, cos θ, tan θ)

38.

If θ is an angle in Quadrant IV, which trig ratios will be positive

a)

sin θ

b)

cos θ

c)

tan θ

d)

cos θ and tan θ

39.

Using reference angles find csc 330^o.

a)

-2

b)

2

c)

1

d)

-1

40.

Using reference angles find the cot 120^o.

a)

-√3/3

b)

√3/3

c)

2

d)

-2

41.

Find a coterminal angle to -180 degrees.

a)

180

b)

90

c)

270

d)

360

42.

Which quadrant is -570⁰

a)

I

b)

II

c)

III

d)

IV

43.

What is the degree equivalent to -135^o

a)

225^o

b)

215^o

c)

235^o

d)

45^o

44.

Formula [Reference angle = Actual angle - 180] is for

a)

quadrant 1

b)

quadrant 2

c)

quadrant 3

d)

quadrant 4

45.

What is the reference angle for -30 degrees?

a)

150 degrees

b)

30 degrees

c)

80 degrees

d)

60 degrees

46.

What is sin(-660)?

a)

root(3)/2

b)

1/2

c)

-1/2

d)

1

47.

What is sin(300)?

a)

1/2

b)

-1/2

c)

root(3)/2

d)

-root(3)/2

48.

In which quadrant would you find an angle measuring -740°

a)

1

b)

2

c)

3

d)

4

49.

In which quadrant is -570⁰

a)

I

b)

II

c)

III

d)

IV

50.

What is the reference angle for 125°?

a)

235°

b)

125°

c)

75°

d)

55°

51.

What is the reference angle for 240°?

a)

60°

b)

30°

c)

45°

d)

210°

52.

-500^o is in which quadrant?

a)

I

b)

II

c)

III

d)

IV

53.

In what quadrant is -285°?

a)

I

b)

II

c)

III

d)

IV

54.

What is the reference angle for 240°?

a)

60°

b)

30°

c)

45°

d)

210°

55.

What is the reference angle for 63°?

a)

117°

b)

207°

c)

63°

d)

153°

56.

What is positive in Q4?

a)

all trig functions

b)

sine

c)

cosine

d)

tangent

57.

What is positive in Q3?

a)

all trig functions

b)

sine

c)

cosine

d)

tangent

58.

What is positive in Q2?

a)

all trig functions

b)

sine

c)

cosine

d)

tangent

59.

What is positive in Q1?

a)

all trig functions

b)

sine

c)

cosine

d)

tangent

60.

Find the reference angle of the angle shown below:

a)

A

b)

B

c)

C

d)

D

61.

Find the reference angle of the angle shown below:

a)

A

b)

B

c)

C

d)

D

62.

Find the reference angle of the angle shown below:

a)

A

b)

B

c)

C

d)

D

63.

Find the reference angle of the angle shown below:

a)

A

b)

B

c)

C

d)

D

64.

Find the exact value of the trig function shown in the image

a)

A

b)

B

c)

C

d)

D

65.

Find the exact value of the trig function shown in the image

a)

A

b)

B

c)

C

d)

D

66.

Find the exact value of the trig function shown in the image

a)

A

b)

B

c)

C

d)

D

67.

Find the exact value of the trig function shown in the image

a)

A

b)

B

c)

C

d)

D

68.

Find the exact value of the trig function shown in the image

a)

A

b)

B

c)

C

d)

D

69.

Find the exact value of the trig function shown in the image

a)

A

b)

B

c)

C

d)

D

70.

Find the exact value of the trig function shown in the image

a)

A

b)

B

c)

C

d)

D

71.

Find the exact value of the trig function shown in the image

a)

A

b)

B

c)

C

d)

D

72.

Use a calculator to evaluate:

$\csc\left(240\degree\ \right)$

Round answer to 4 decimal places

73.

Use a calculator to evaluate:

$\cot\left(\frac{\ -4\pi}{3}\right)$

Round answer to 4 decimal places

74.

Evaluate the trigonometric function without using a calculator. Angles are given in degrees.

cos 135

a)

$45$

b)

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

c)

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

d)

-45

75.

Evaluate the trigonometric function without using a calculator. Angles are given in degrees.

tan (-30)

a)

30

b)

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

c)

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

d)

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

76.

Evaluate the trigonometric function without using a calculator. Angles are given in degrees.

sin 480

a)

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

b)

60

c)

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

d)

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

77.

Evaluate the trigonometric function without using a calculator. Angles are given in degrees.

cos 720

a)

0

b)

1

c)

-1

78.

Evaluate the trigonometric function without using a calculator. Angles are given in degrees.

$\cos\frac{7\pi}{4}$

a)

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

b)

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

c)

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

d)

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

79.

Evaluate the trigonometric function without using a calculator. Angles are given in degrees.

\sin\left(-\frac{\pi}{2}\right)

a)

1

b)

0

c)

-1

80.

Evaluate the trigonometric function without using a calculator. Angles are given in degrees.

$\tan\left(-\frac{10\pi}{3}\right)$

a)

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

b)

$-\sqrt{3}$

c)

$\sqrt{3}$

d)

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

81.

Evaluate the trigonometric function without using a calculator. Angles are given in degrees.

$\tan\ \frac{16\pi}{3}$

a)

$\sqrt{3}$

b)

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

c)

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

d)

$-\sqrt{3}$

82.

Use a calculator to evaluate the trigonometric function of the angle given in degrees. Round to the nearest hundredths place.

sin 132

a)

0.7431

b)

0.743

c)

0.744

d)

0.74

83.

Use a calculator to evaluate the trigonometric function of the angle given in degrees. Round to the nearest hundredths place.

cos (-203)

a)

0.921

b)

-0.920

c)

-0.921

d)

-0.92

84.

$\sin\ \left(\frac{5}{8}\pi\right)$

Use a calculator to evaluate the trigonometric function of the angle given in radians. Round to the nearest hundredths place.

a)

0.923

b)

0.034

c)

0.924

d)

0.0343

85.

$\cos\left(1.2\pi\right)$

Use a calculator to evaluate the trigonometric function of the angle given in degrees. Round to the nearest hundredths place.

a)

0.997

b)

-0.809

c)

0.809

d)

0.998

86.

Using $\left(2,\ -3\sqrt{2}\right)$ as the terminal side, what is $\sec\left(\theta\right)$ ?

a)

$\frac{\sqrt{22}}{11}$

b)

$\frac{\sqrt{22}}{2}$

c)

$-\frac{3\sqrt{11}}{11}$

d)

$-\frac{\sqrt{11}}{3}$

87.

The special right triangles are:

a)

A right triangle with two acute angles

b)

A right triangle with an acute angle of 30 degrees.

c)

A right triangle with an acute angle of 45 degrees.

d)

A right triangle with an acute angle of 60 degrees.

e)

A right triangle with an acute angle of 90 degrees.

88.

Use a calculator to evaluate the trigonometric function. Round your answer to four decimal places.

\csc\left(\frac{2\pi}{9}\right)

a)

0.6428

b)

0.7660

c)

0.9999

d)

1.5557

89.

Convert the given angle measure from radians to degrees. Round to three decimal places.

5.07

a)

$0.088\degree$

b)

$290.490\degree$

c)

$580.979\degree$

d)

$145.245\degree$

90.

a)

$-\frac{25}{7}$

b)

$\frac{25}{7}$

c)

$-\frac{7}{25}$

d)

$\frac{7}{25}$

91.

Evaluate the trigonometric function.

\sin\left(\frac{-14\pi}{3}\right)

a)

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

b)

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

c)

$\frac{1}{2}$

d)

$-\frac{1}{2}$

92.

Rewrite the given angle in radian measure.

-60\degree

a)

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

b)

$-\pi$

c)

$-\frac{\pi}{6}$

d)

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

93.

Use a calculator to evaluate the trig function. Round your answer to 4 decimal places.

tan 10.7

a)

0.1857

b)

-0.9566

c)

-0.2913

d)

3.2841

94.

Use a calculator to evaluate the trig function. Round your answer to 4 decimal places.

\cos\left(-\frac{7\pi}{5}\right)

a)

0.9511

b)

-0.3090

c)

-0.0767

d)

1.0515

95.

Determine the quadrant in which the angle lies.

\frac{3\pi}{4}

a)

Quadrant I

b)

Quadrant II

c)

Quadrant III

d)

Quadrant IV

96.

Determine the quadrant in which the angle lies.
$-135\degree$

a)

Quadrant I

b)

Quadrant II

c)

Quadrant III

d)

Quadrant IV

97.

Use a calculator to evaluate the trig function. Round your answer to 4 decimal places.

$\cot\left(-\frac{2\pi}{9}\right)$

a)

-0.0122

b)

-0.8391

c)

0.9999

d)

-1.1918

98.

Which of the following are trig functions for the terminal side passing through the point (-3,4)?

SELECT ALL THAT APPLY

a)

$\tan\theta\ =\frac{\ -4}{3}$

b)

$\cot\theta\ =\frac{\ -4}{3}$

c)

$\sec\theta\ =\frac{\ -5}{3}$

d)

$\csc\theta\ =\frac{\ -5}{4}$

99.

Which of the following are trig functions for the terminal side passing through the point (-4,3)?

SELECT ALL THAT APPLY

a)

$\tan\theta\ =\frac{\ -4}{3}$

b)

$\cot\theta\ =\frac{\ -3}{4}$

c)

$\sec\theta\ =\frac{\ -5}{4}$

d)

$\csc\theta\ =\frac{\ -5}{3}$

100.

Which of the following are trig functions for the terminal side passing through the point (-4,-3)?

SELECT ALL THAT APPLY

a)

$\tan\theta\ =\frac{\ 3}{4}$

b)

$\cot\theta\ =\frac{\ -3}{4}$

c)

$\sec\theta\ =\frac{\ -5}{4}$

d)

$\csc\theta\ =\frac{\ -5}{3}$

101.

Which of the following are trig functions for the terminal side passing through the point (5,12)?

SELECT ALL THAT APPLY

a)

$\tan\theta\ =\frac{\ 12}{5}$

b)

$\cot\theta\ =\frac{\ 5}{12}$

c)

$\sec\theta\ =\frac{\ -5}{13}$

d)

$\csc\theta\ =\frac{\ -12}{13}$

102.

Which of the following are trig functions for the terminal side passing through the point (6,-8)?

SELECT ALL THAT APPLY

a)

$\tan\theta\ =\ \frac{\ -4}{3}$

b)

$\cot\theta\ =\ \frac{\ -3}{4}$

c)

$\sec\theta\ =\ \frac{\ 3}{5}$

d)

$\csc\theta\ =\frac{\ -4}{5}$

103.

What is the reciprocal of the sine function?

a)

cosecant

b)

cosine

c)

secant

d)

cotangent

104.

Secant is the reciprocal of what function?

a)

Cosecant

b)

Sine

c)

Cosine

d)

Tangent

105.

Cotangent is the reciprocal of what function?

a)

Cosecant

b)

Sine

c)

Cosine

d)

Tangent

106.

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

a)

-2/3

b)

-3/2

c)

3/2

d)

2/3

107.

Given the Csc(x) = 1, then the Sin(x) = ?

a)

1

b)

-1

c)

0

d)

Undefined

108.

Find secΘ.

a)

17/15

b)

15/17

c)

8/17

d)

17/8

109.

Find cotΘ.

a)

3/4

b)

4/3

c)

5/4

d)

5/3

110.

Find cscΘ.

a)

15/17

b)

17/15

c)

8/17

d)

17/8

111.

Write all six trig ratios.

a)

$\sin\theta=\frac{24}{25}\ \cos\theta=\frac{7}{25}\ \tan\theta=\frac{24}{7}\$ $\csc\theta=\frac{25}{24}\ \sec\theta=\frac{25}{7}\ \cot\theta=\frac{7}{24}$

b)

$\sin\theta=\frac{7}{25}\ \cos\theta=\frac{24}{25}\ \tan\theta=\frac{7}{24}$ $\csc\theta=\frac{25}{7}\ \sec\theta=\frac{25}{24}\ \cot\theta=\frac{24}{7}$

112.

Solve for DE

a)

36.5

b)

18.8

c)

8.5

d)

7.9

113.

In which two quadrants is inverse sine defined?

a)

Quadrant I

b)

Quadrant II

c)

Quadrant III

d)

Quadrant IV

114.

In which two quadrants is inverse cosine defined?

a)

Quadrant I

b)

Quadrant II

c)

Quadrant III

d)

Quadrant IV

115.

In which two quadrants is inverse tangent defined?

a)

Quadrant I

b)

Quadrant II

c)

Quadrant III

d)

Quadrant IV

116.

True or False: $\arcsin\left(x\right)$ is another way to write $\sin^{-1}\left(x\right)$ .

a)

TRUE!

b)

FALSE!

117.

Evaluate the expression in RADIANS. Give your answer to the hundredths place.

$\sin^{-1}\left(0.72\right)=$

(a)

118.

Evaluate the expression in RADIANS. Give your answer to the hundredths place.

$\arccos\left(1\right)=$

(a)

119.

Evaluate the expression in RADIANS. Give your answer to the hundredths place.

$\cos^{-1}\left(-0.27\right)=$

(a)

120.

Evaluate the expression in RADIANS. Give your answer to the hundredths place.

$\arctan\left(-1.73\right)=$

(a)

121.

Evaluate the inverse trig function USING THE UNIT CIRCLE. Give your answer in DEGREES.

$\sin^{-1}\left(-\frac{\sqrt[]{3}}{2}\right)$

a)

$45\degree$

b)

$300\degree$

c)

$30\degree$

d)

$315\degree$

122.

Evaluate the inverse trig function USING THE UNIT CIRCLE. Give your answer in DEGREES.

$\arcsin\left(\frac{1}{2}\right)=$

a)

$45\degree$

b)

$60\degree$

c)

$30\degree$

d)

$90\degree$

123.

Evaluate the inverse trig function USING THE UNIT CIRCLE. Give your answer in DEGREES.

$\cos^{-1}\left(-\frac{1}{2}\right)=$

a)

$240\degree$

b)

$60\degree$

c)

$150\degree$

d)

$120\degree$

124.

Evaluate the inverse trig function USING THE UNIT CIRCLE. Give your answer in DEGREES.

$\arccos\left(-\frac{\sqrt[]{2}}{2}\right)$

a)

$180\degree$

b)

$135\degree$

c)

$150\degree$

d)

$120\degree$

125.

Evaluate the inverse trig function USING THE UNIT CIRCLE. Give your answer in DEGREES.

$\arctan\left(\sqrt[]{3}\right)$

a)

$60\degree$

b)

$300\degree$

c)

$270\degree$

d)

$30\degree$

126.

Evaluate the inverse trig function USING THE UNIT CIRCLE. Give your answer in DEGREES.

$\tan^{-1}\left(-1\right)=$

a)

$45\degree$

b)

$330\degree$

c)

$270\degree$

d)

$315\degree$

127.

Find $m\angle C$ . Give your answer in DEGREES to the hundredths place. (Note: drawing is NOT to scale).

a)

$90\degree$

b)

$68.32\degree$

c)

$73.74\degree$

d)

$70.48\degree$

128.

Find $m\angle T$ . Give your answer in DEGREES to the hundredths place. (Note: drawing is NOT to scale).

a)

$25.22\degree$

b)

$16.26\degree$

c)

$73.74\degree$

d)

$35.47\degree$

129.

a)

-π/3

b)

4π/3

c)

-2π/3

d)

2π/3

130.

a)

0

b)

π/2

c)

2π

d)

3π

131.

a)

3π/4

b)

π/4

c)

5π/4

d)

-3π/4

132.

a)

π/6

b)

5π/6

c)

7π/6

d)

2π

133.

a)

π/2

b)

π

c)

3π/2

d)

-3π/2

134.

Evaluate the function: arcsin(-1/2)

a)

π/3

b)

π/6

c)

5π/6

d)

-π/6

135.

arccos (-√3/2)

a)

5π/6

b)

2π/3

c)

-π/6

d)

7π/6

136.

What is tan[arccos(-1)]?

a)

undefined

b)

0

c)

½

d)

1

137.

Evaluate the function: tan[sin^-1(-1/2)]

a)

√3

b)

√3/3

c)

-√3

d)

-√3/3

138.

cos^-1[tan(-π/4)] =

a)

0

b)

π

c)

π/4

d)

3π/4

139.

What is the RANGE of angles for inverse sine?

a)

[0, π]

b)

[-1, 1]

c)

[-π/2, π/2]

d)

(-∞, ∞)

140.

What RANGE of angles for inverse cosine?

a)

[0, π]

b)

(-∞, ∞)

c)

[-π/2, π/2]

d)

[-1, 1]

141.

What is the RANGE of angles for inverse tangent?

a)

[-π/2, π/2]

b)

(-π/2, π/2)

c)

[0, π]

d)

(-∞, ∞)

142.

What is the period
of
y = 3 sin 2x?

a)

2

b)

3

c)

180

d)

360

143.

What is the amplitude of y = 3 cos 2x?

a)

3

b)

2

c)

90
90⁰

d)

350⁰

144.

$-2\sqrt[]{3}=-4\cos x$

a)

$\frac{\pi}{6},\frac{5\pi}{6}$

b)

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

c)

$\frac{\pi}{6}$

d)

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

145.

$\sec\theta-2=-\frac{3}{2}$

a)

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

b)

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

c)

No solution

146.

$-3\cot x=\sqrt[]{3}$

a)

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

b)

$\frac{2\pi}{3},\ \frac{5\pi}{3}$

c)

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

d)

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

147.

$\tan x=\tan x\sin x$

a)

$x=0,\ \frac{\pi}{2},\ \pi$

b)

$x=0,\ \pi$

c)

$x=0,\ \frac{\pi}{2}$

d)

No solution.

148.

$3\csc^2x=4+2\csc^2x$

a)

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

b)

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

c)

$x=\frac{\pi}{6},\ \frac{5\pi}{6},\ \frac{7\pi}{6},\ \frac{11\pi}{6}$

d)

No solution.

149.

$2\cos^2x=3\cos x-1$

a)

$x=0,\ \frac{\pi}{6},\ \frac{11\pi}{6}$

b)

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

c)

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

d)

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

150.

$4-\csc^2\theta=4\csc\theta-2\csc^2\theta$

a)

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

b)

$x=\frac{\pi}{6},\ \frac{5\pi}{6},\ \frac{7\pi}{6},\ \frac{11\pi}{6}$

c)

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

d)

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

151.

$\sec^2x=-2\tan x$

a)

$x=\frac{\pi}{4},\ \frac{5\pi}{4}$

b)

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

c)

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

d)

No solution.

152.

Challenge! The equation $9^{\sin\theta}=3$ has two solutions. One of them is $30\degree$ . Find the other one.

a)

$210\degree$

b)

$150\degree$

c)

$60\degree$

d)

$330\degree$

153.

$1+2\sin x=\csc x$

a)

$\frac{\pi}{6},\ \frac{5\pi}{6},\ \frac{3\pi}{2}$

b)

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

c)

$\frac{\pi}{6},\ \frac{\pi}{2},\ \frac{5\pi}{6}$

d)

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

154.

Solve each equation using a calculator. Round to the nearest hundredth.

$4+3\cos x=3.06+2\cos x$

a)

$35.90\degree,\ 160.05\degree\$

b)

$199.95\degree$

c)

$160.05\degree,\ 199.95\degree$

d)

No solution.

155.

Solve each equation using a calculator. Round to the nearest hundredth. $5+4\cot\theta=12.72$

a)

$264.86\degree$

b)

$27.39\degree,\ 207.39\degree$

c)

$27.39\degree,\ 264.86\degree$

d)

No solution.

156.

Solve using a calculator. Round to the nearest degree.

$3\sin^2x+2\sin x-1=0$

a)

$19\degree,\ 161\degree,\ 270\degree$

b)

$19\degree,\ 161\degree$

c)

$19\degree,\ 270\degree$

d)

$199\degree,\ 270\degree,\ 341\degree$

157.

Solve using a calculator. Round to the nearest hundredth.

$\sec^2x+4\sec x=5$

a)

$x=90\degree,\ 101.54\degree,\ 258.46\degree$

b)

$x=0\degree,\ 78.46\degree,\ 101.54\degree$

c)

$x=0\degree,\ 101.54\degree,\ 258.46\degree$

d)

$x=0\degree,\ 101.54\degree$

158.

Solve using a calculator. Round your answers to the nearest hundredth. $3\sin x-14=24\csc x$

a)

$x=228.59\degree,\ 311.41\degree$

b)

No solution.

c)

$x=48.59\degree,\ 131.41\degree$

d)

$x=48.59\degree,\ 311.41\degree$

159.

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

a)

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

b)

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

c)

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

d)

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

160.

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)

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

161.

Solve equation for $0\le\theta<2\pi$ .
$-2=-5+3\sec\theta$

a)

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

b)

$\theta=0$

c)

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

d)

$No\ Solution$

162.

Solve equation for $0\le\theta<2\pi$ .
$4+4\tan\theta=0$

a)

$\theta=\pi$

b)

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

c)

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

d)

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

163.

Solve equation for $0\le\theta<2\pi$ .
$2=-4-3\csc\theta$

a)

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

b)

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

c)

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

d)

$\theta=\frac{2\pi}{3},\frac{7\pi}{6},\frac{11\pi}{6}$

164.

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)

$\theta=0,\pi$

165.

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

a)

$\theta=\frac{\pi}{6},\frac{5\pi}{6},\frac{7\pi}{6},\frac{11\pi}{6}$

b)

$\theta=\frac{\pi}{3},\frac{2\pi}{3},\frac{4\pi}{3},\frac{5\pi}{3}$

c)

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

d)

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

166.

Solve equation for $0\le\theta<2\pi$ .
$3\sin^2\theta+4=5+\sin^2\theta$

a)

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

b)

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

c)

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

d)

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

167.

Solve equation for $0\le\theta<2\pi$ .
$-3=\cot^2\theta-6$

a)

$\theta=\frac{\pi}{6},\frac{7\pi}{4},\frac{11\pi}{6}$

b)

$\theta=\frac{7\pi}{6},\frac{5\pi}{4},\frac{11\pi}{6}$

c)

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

d)

$\theta=\frac{\pi}{6},\frac{5\pi}{6},\frac{7\pi}{6},\frac{11\pi}{6}$

168.

Solve equation for $0\le\theta<2\pi$ .
$4+\csc^2\theta=2\csc^2\theta$

a)

$\theta=\frac{5\pi}{6},\frac{4\pi}{3}$

b)

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

c)

$\theta=\frac{\pi}{6},\frac{5\pi}{6},\frac{7\pi}{6},\frac{11\pi}{6}$

d)

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

169.

Solve equation for $0\le\theta<2\pi$ .
$-\sin\theta\csc\theta+3\csc\theta=\sqrt{2}\sin\theta+3\csc\theta$

a)

$\theta=\frac{5\pi}{4},\frac{11\pi}{6}$

b)

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

c)

$\theta=0,\pi,\frac{5\pi}{4},\frac{7\pi}{4}$

d)

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

170.

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

a)

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

b)

$\theta=\frac{\pi}{2},\frac{7\pi}{6},\frac{3\pi}{2},\frac{11\pi}{6}$

c)

$\theta=0,\pi,\frac{4\pi}{3},\frac{5\pi}{3}$

d)

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

171.

Solve equation for $0\le\theta<2\pi$ .
$0=-3\cot\theta+2\sqrt{3}\cot\theta\sin\theta$

a)

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

b)

$\theta=0,\frac{5\pi}{6},\pi,\frac{11\pi}{6}$

c)

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

d)

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

172.

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

a)

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

b)

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

c)

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

d)

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

173.

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)

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

174.

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)

$\theta=0$

175.

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)

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

176.

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)

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

177.

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

a)

$\theta=\frac{3\pi}{2},\frac{11\pi}{6}$

b)

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

c)

$\theta=\frac{7\pi}{6},\frac{3\pi}{2},\frac{11\pi}{6}$

d)

$\theta=\frac{\pi}{4},\frac{11\pi}{6}$

178.

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

a)

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

b)

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

c)

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

d)

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

179.

Find the EXACT value

$\cos\left[\tan^{-1}\left(\sqrt{\left(\ 3\right)}\right)\right]$

180.

Find the EXACT value

$\sec\left[\cos^{-1}\left(\frac{\ \sqrt{\ 3}}{2}\right)\right]$

181.

Find the EXACT value

$\sec^{-1}\left[\sin\left(\ \frac{\ \pi}{3}\right)\right]$

182.

Find the EXACT value

$\cot^{-1}\left[\tan\left(\ \frac{\ \pi}{2}\right)\right]$

Unit 10 Test review

Total questions: 182

Worksheet time: 3hrs 34mins

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