Free Printable Precalc Final Review: Trigonometry

1.

Which of the following is closest to the measure of the angle shown?

a)

7/10 π

b)

3/8 π

c)

7/20 π

d)

3/2 π

2.

What are the negative and positive coterminal angles of 240 degrees?

a)

540°, -120°

b)

600°, -120°

c)

425°, -240°

d)

120°, -135°

3.

The unit circle...

a)

Has center at (1,1)

b)

Has a circumference of 1

c)

Has a diameter of 1

d)

Has a radius of 1

4.

Based on the unit circle, what is the value of cos?

a)

y/r

b)

x/r

c)

r/y

d)

y/x

5.

Based on the unit circle, what is the value of tan?

a)

y/r

b)

x/r

c)

r/y

d)

y/x

6.

Based on the unit circle, what is the value of sin?

a)

y/r

b)

x/r

c)

r/y

d)

y/x

7.

What is cos 60°?

a)

½

b)

^√3/₂

c)

^√2/₂

d)

1

8.

What is sin 45°?

a)

1

b)

^√3/₂

c)

½

d)

^√2/₂

9.

What is sin 30°?

a)

^√3/₂

b)

1

c)

½

d)

^√2/₂

10.

cosθ is positive in

a)

the 1st and 2nd quadrants

b)

the 1st and 3rd quadrants

c)

the 1st and 4th quadrants

d)

the 2nd and 3rd quadrants

11.

sinθ is positive in

a)

the 1st and 2nd quadrants

b)

the 1st and 3rd quadrants

c)

the 1st and 4th quadrants

d)

the 2nd and 3rd quadrants

12.

What is the exact value of sin 150°

a)

-1/2

b)

-√3/2

c)

1/2

d)

√3/2

13.

What are the coordinates of 210° on the unit circle?

a)

(−√3/2, −1/2)

b)

(√3/2, −1/2)

c)

(−√3/2, 1/2)

d)

(−1/2,−√3/2 )

14.

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

a)

1

b)

2

c)

3

d)

4

15.

What is the reference angle for 125°?

a)

235°

b)

125°

c)

75°

d)

55°

16.

What is the reference angle for -30°?

a)

150°

b)

30°

c)

80°

d)

60°

17.

Standard position is when .....

a)

the initial side of the angle is on the positive x-axis.

b)

the initial side of the angle is on the negative x-axis.

c)

the initial side of the angle is on the positive y-axis.

d)

the initial side of the angle is on the negative y-axis.

18.

Negative angles are measured in which direction from standard position?

a)

Clockwise

b)

Counterclockwise

19.

Positive angles are measured in which direction from standard position?

a)

Clockwise

b)

Counterclockwise

20.

In what quadrant is -285°?

a)

I

b)

II

c)

III

d)

IV

21.

What type of circle plays a large role in understanding trig functions?

a)

An elliptic circle

b)

The unit circle

c)

The perfect circle

d)

The Pythagorean circle

22.

What are the 3 basic trig functions?

a)

Sine, cosine, and cotangent

b)

Sine, cotangent, and cosecant

c)

Sine, cosine, and tangent

d)

Cosecant, cosine, and cotangent

23.

The cosine represents the x-coordinate.

a)

True

b)

False

24.

All six trigonometric functions are positive in the first quadrant.

a)

True

b)

False

25.

What is the reference angle?

a)

38

b)

52

c)

142

d)

398

26.

What is the reference angle?

a)

38

b)

52

c)

142

d)

398

27.

All six trigonometric functions are positive in the first quadrant.

a)

True

b)

False

28.

Find sec(π/4)

a)

0

b)

-2

c)

√2

d)

-√3

29.

Find csc(7π/6)

a)

0

b)

-2

c)

√2

d)

-√3

30.

Find tan(π)

a)

0

b)

-2

c)

√2

d)

-√3

31.

Which function is the reciprocal function of the cosine?

a)

sine

b)

cosecant

c)

secant

d)

tangent

32.

Which function is the reciprocal of the sine?

a)

cosine

b)

secant

c)

cotangent

d)

cosecant

33.

sin^-1(-1/2)

a)

π/3

b)

π/6

c)

5π/6

d)

-π/6

34.

cos^-1(√(3)/2)

a)

π/3

b)

2π/3

c)

π/6

d)

5π/6

35.

sec^-1(-2)

a)

π/3

b)

2π/3

c)

π/6

d)

5π/6

36.

tan^-1(√(3))

a)

π/3

b)

2π/3

c)

π/6

d)

5π/6

37.

Domain of function $\sin^{-1}x\ is$

a)

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

b)

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

c)

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

d)

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

38.

Domain of function $\cos^{-1}x\ is$

a)

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

b)

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

c)

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

d)

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

39.

Range of function $\sin^{-1}x\ is$

a)

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

b)

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

c)

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

d)

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

40.

Range of function $\cos^{-1}x\ is$

a)

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

b)

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

c)

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

d)

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

41.

Range of function $\tan^{-1}x\ is$

a)

R

b)

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

c)

$R-\left\{\frac{\pi}{2}\right\}$

d)

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

42.

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

a)

$\sqrt{3}$

b)

$-\sqrt{3}$

c)

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

d)

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

43.

cos^-1(√(3)/2)

a)

$\frac{\pi}{3}$

b)

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

c)

$\frac{\pi}{6}$

d)

$\frac{\pi}{4}$

44.

cos^-1(tan(-π/4))

a)

0

b)

π

c)

π/4

d)

3π/4

45.

The value of $\cos^{-1}\left(-\frac{\sqrt{3}}{2}\right)\$ is

a)

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

b)

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

c)

$\frac{\pi}{6}$

d)

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

46.

What is cos^-1(½)?

a)

¼π, 45⁰

b)

⅓π, 60⁰

c)

½π, 90⁰

d)

π, 180⁰

47.

tan(sin^-1(1))=

a)

undefined

b)

0

c)

½

d)

1

48.

tan(sin^-1(1))=

a)

undefined

b)

0

c)

½

d)

1

49.

What type of circle plays a large role in understanding trig functions?

a)

An elliptic circle

b)

The unit circle

c)

The perfect circle

d)

The Pythagorean circle

50.

What are the 3 basic trig functions?

a)

Sine, cosine, and cotangent

b)

Sine, cotangent, and cosecant

c)

Sine, cosine, and tangent

d)

Cosecant, cosine, and cotangent

51.

The cosine represents the x-coordinate.

a)

True

b)

False

52.

All six trigonometric functions are positive in the first quadrant.

a)

True

b)

False

53.

What is the reference angle?

a)

38

b)

52

c)

142

d)

398

54.

What is the reference angle?

a)

115

b)

65

c)

25

d)

155

55.

What is the reference angle?

a)

163

b)

73

c)

27

d)

107

56.

Find sec(π/4)

a)

0

b)

-2

c)

√2

d)

-√3

57.

Find csc(7π/6)

a)

0

b)

-2

c)

√2

d)

-√3

58.

Find tan(π)

a)

0

b)

-2

c)

√2

d)

-√3

59.

Which function is the reciprocal function of the cosine?

a)

sine

b)

cosecant

c)

secant

d)

tangent

60.

Which function is the reciprocal of the sine?

a)

cosine

b)

secant

c)

cotangent

d)

cosecant

61.

State a Pythagorean Identity

a)

a²+b²=c²

b)

sin²x+cos²x=1

c)

tan x=sin/cos

d)

sin x =1/cosx

62.

Let (–3, 4) be a point on the terminal side of an angle θ in standard position. Find the exact values of sin θ, cos θ, and tan θ.

a)

$\sin\theta=-\frac{3}{5},\ \cos\theta=-\frac{4}{5},\ \tan\theta=-\frac{3}{4}$

b)

$\sin\theta=\frac{4}{5},\ \cos\theta=-\frac{3}{4},\ \tan\theta=-\frac{4}{3}$

c)

$\sin\theta=-\frac{3}{4},\ \cos\theta=\frac{4}{5},\ \tan\theta=-\frac{4}{3}$

d)

$\sin\theta=\frac{4}{5},\ \cos\theta=-\frac{3}{5},\ \tan\theta=-\frac{3}{4}$

63.

*

a)

csc x

b)

sec x

c)

cot x

d)

tan x

64.

*

a)

cos x

b)

csc x

c)

sec x

d)

cot x

65.

*

a)

sin x

b)

cos x

c)

tan x

d)

csc x

66.

*

a)

sin x

b)

cos x

c)

csc x

d)

cot x

67.

*

a)

tan² x

b)

cos² x

c)

cot² x

d)

csc² x

68.

*

a)

csc² x

b)

cot² x

c)

sin² x

d)

sec² x

69.

Which expression is always equivalent to sin x when 0°< x < 90°?

a)

cos(90°−x)

b)

cos(45°−x)

c)

cos(2x)

d)

cos x

70.

Find the cofunction of
csc(25^o)

a)

sec(25^o)

b)

sec(65^o)

c)

csc(65^o)

d)

sin(25^o)

71.

Find the cofunction of
sin(42^o)=

a)

cos(42^o)

b)

cos(48^o)

c)

csc(48^o)

d)

csc(42^o)

72.

Find the cofunction of cos(15^o)

a)

sin(75^o)

b)

sec(75^o)

c)

csc(75^o)

d)

cot(75^o)

73.

Find the cofunction of
sec(17^o)=

a)

sin(73^o)

b)

cos(73^o)

c)

csc(17^o)

d)

csc(73^o)

74.

Find the cofunction of cot 50°

a)

tan 50°

b)

cot 40°

c)

tan 40°

d)

Cot 50^o

75.

Solve for 0≤x≤2π

2cos²x + cosx = 0

a)

π/2, 3π/2

b)

0, π,2π

c)

2π/3, 4π/3

d)

π/3, 5π/3

76.

Solve for 0≤x≤2π

4cos²x- 2 = 0

a)

π/3, 5π/3

b)

π/4, 7π/4

c)

3π/4, 5π/4

d)

π/6, 11π/6

77.

Solve for 0≤x≤2π

sinxtanx = sinx

a)

π/2, 3π/2

b)

3π/4, 7π/4

c)

0, π, 2π

d)

π/4, 5π/4

78.

Solve for 0≤x≤2π

2sin²x - 5sinx + 2 = 0

a)

π/6, 5π/6

b)

7π/6, 11π/6

c)

π/3, 2π/3

d)

4π/3, 5π/3

79.

Solve for 0≤x≤2π

(cotx - √3) (cscx + 2)

a)

π/6

b)

5π/6

c)

7π/6

d)

11π/6

80.

Solve for 0≤x≤2π

2sin²x - sinx = 0

a)

0, π, 2π

b)

π/2, 3π/2

c)

π/6, 5π/6

d)

π/3, 2π/3

81.

Solve for 0≤x≤2π

3sin²x + sinx - 4 = 0

a)

0, π

b)

π/2

c)

π/6, 5π/6

d)

3π/2

82.

Solve
cosθ = - √(3)/2
on θ∈[0, 2π)

a)

θ = π /3, 2π /3

b)

θ = 2π /3, 4π /3

c)

θ = π /6, 5π /6

d)

θ = 5π /6, 7π /6

83.

Which of the following is the solution of sin²x + cos²x = 2?

a)

0

b)

π/4

c)

π/6

d)

no solution

84.

Solve sinθ = -1 on θ∈[0, 2π)

a)

θ = π /2, 3π /2

b)

θ = π /2

c)

θ = 3π /2

d)

θ = π

85.

Solve sinθ = ½ on θ∈[0, 2π)

a)

θ = π / 6, 7π / 6

b)

θ = π / 6, 5π / 6

c)

θ = 5π / 6, 7π / 6

d)

θ = 7π / 6, 11π / 6

86.

Solve
2cos²θ -1=0
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

87.

Solve

sin²θ = 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

88.

Find all solutions.

2sin(6x) + √3 = 0

a)

x = π/18 + πn/3 and x = 5π/18 + πn/3

b)

x = 11π/18 + 2πn and x = 7π/18 + 2πn

c)

x = 4π/18 + πn/3 and x = 5π/18 + πn/3

d)

x = 4π/3 + 2πn and x = 5π/3 + 2πn

89.

$Solve\ 2\cos⁡x=\sqrt{3}\ for\ 0≤x≤360°$

a)

30, 330

b)

60, 300

c)

150, 210

d)

120, 240

90.

$Solve\cos⁡2x=-\frac{\sqrt{3}}{2}\ for\ 0≤x≤360°$

a)

150, 210

b)

120, 150, 300, 330

c)

45, 315

d)

75, 105, 255, 285

91.

$Solve\sqrt{2}\cos⁡x-1=0\ for\ 0≤x≤360°$

a)

45, 225

b)

45, 135

c)

135, 225

d)

45, 315

92.

$Solve\sqrt{2}\cos⁡x-1=0\ for\ 0≤x≤360°$

a)

45, 225

b)

45, 135

c)

135, 225

d)

45, 315

93.

$Solve\ 2\sin x-1=0\ for\ 0≤x≤360°$

a)

30, 150

b)

60, 120

c)

45, 225

d)

90, 270

94.

$Solve\ \sin3⁡x=-\frac{1}{\sqrt{2}}\ for\ 0≤x≤360°$

a)

225, 315

b)

75, 105, 195, 225, 315, 345

c)

45, 75, 165, 195, 285, 315

d)

135, 225

95.

$Solve\cos⁡3x=0\ for\ 0≤x≤360°$

a)

0, 60, 120, 180, 240, 300

b)

30, 90, 120, 150, 270, 330

c)

0, 30, 150, 210, 240, 330

d)

30, 90, 150, 210, 270, 330

96.

$Solve\sin2⁡x=\frac{\sqrt{3}}{2}\ for\ 0≤x≤360°$

a)

30, 150

b)

30, 60, 210, 240

c)

60, 120

d)

15, 75, 195, 255

97.

$Solve\sin2x=\frac{1}{2}\ for\ 0≤x≤360°$

a)

60, 120

b)

30, 150

c)

30, 60, 210, 240

d)

15, 75, 195, 255

98.

$Solve\cos⁡x=-1\ for\ 0≤x≤360°$

a)

270

b)

0

c)

90

d)

180

99.

$Solve\sin⁡x=1\ for\ 0≤x≤360°$

a)

90

b)

270

c)

0

d)

180

100.

$Solve\cos⁡x=-\frac{1}{\sqrt{2}}\ for\ 0≤x≤360°$

a)

135, 45

b)

150, 210

c)

135, 225

d)

30, 330

101.

$Solve\cos⁡x=-\frac{1}{2}\ for\ 0≤x≤360°$

a)

120, 240

b)

120, 60

c)

60, 300

d)

240, 300

102.

$Solve\ \sin x=\frac{1}{2}\ for\ 0\le x\le360\degree$

a)

30, 330

b)

30, 150

c)

60, 120

d)

60, 300

103.

$Solve\sin x=\frac{\sqrt{3}}{2}\ for\ 0≤x≤360°$

a)

30, 150

b)

60, 300

c)

30, 330

d)

60, 120

104.

Which of the following is closest to the measure of the angle shown?

a)

7/10 π

b)

3/8 π

c)

7/20 π

d)

3/2 π

105.

Which of the following is closest to the measure of the angle drawn by the green curve?

a)

5/6 π

b)

5/3 π

c)

4/5 π

d)

4/3 π

106.

What are the negative and positive coterminal angles of 240 degrees?

a)

540°, -120°

b)

600°, -120°

c)

425°, -240°

d)

120°, -135°

107.

The unit circle...

a)

Has center at (1,1)

b)

Has a circumference of 1

c)

Has a diameter of 1

d)

Has a radius of 1

108.

What is the exact coordinates of 3π/4 on the unit circle?

a)

(−√2∕2, √2∕2)

b)

(−√2∕2, −√2∕2)

c)

(−√3∕2, −√2∕2)

d)

(√2∕2, −√2∕2)

109.

Based on the unit circle, what is the value of cos?

a)

y/r

b)

x/r

c)

r/y

d)

y/x

110.

Based on the unit circle, what is the value of tan?

a)

y/r

b)

x/r

c)

r/y

d)

y/x

111.

What is cos 60°?

a)

½

b)

^√3/₂

c)

^√2/₂

d)

1

112.

What is sin 45°?

a)

1

b)

^√3/₂

c)

½

d)

^√2/₂

113.

What is sin 30°?

a)

^√3/₂

b)

1

c)

½

d)

^√2/₂

114.

cosθ is positive in

a)

the 1st and 2nd quadrants

b)

the 1st and 3rd quadrants

c)

the 1st and 4th quadrants

d)

the 2nd and 3rd quadrants

115.

sinθ is positive in

a)

the 1st and 2nd quadrants

b)

the 1st and 3rd quadrants

c)

the 1st and 4th quadrants

d)

the 2nd and 3rd quadrants

116.

What is the exact value of sin 150°

a)

-1/2

b)

-√3/2

c)

1/2

d)

√3/2

117.

What are the coordinates of 210° on the unit circle?

a)

(−√3/2, −1/2)

b)

(√3/2, −1/2)

c)

(−√3/2, 1/2)

d)

(−1/2,−√3/2 )

118.

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

a)

1

b)

2

c)

3

d)

4

119.

What is the reference angle for 125°?

a)

235°

b)

125°

c)

75°

d)

55°

120.

What is the reference angle for -30°?

a)

150°

b)

30°

c)

80°

d)

60°

121.

Standard position is when .....

a)

the initial side of the angle is on the positive x-axis.

b)

the initial side of the angle is on the negative x-axis.

c)

the initial side of the angle is on the positive y-axis.

d)

the initial side of the angle is on the negative y-axis.

122.

Negative angles are measured in which direction from standard position?

a)

Clockwise

b)

Counterclockwise

123.

Positive angles are measured in which direction from standard position?

a)

Clockwise

b)

Counterclockwise

124.

In what quadrant is -285°?

a)

I

b)

II

c)

III

d)

IV

Precalc Final Review: Trigonometry

Total questions: 124

Worksheet time: 3hrs 28mins

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