Free Printable Intro to Trig

1.

What is the value of sine at 30

a)

1/2

b)

√3 / 2

c)

0

d)

√2 ⁄ 2

2.

What is the value of cosine at 0

a)

0

b)

1/2

c)

1

d)

√3 / 2

3.

What is the value of sine at 30

a)

1/2

b)

√3 / 2

c)

0

d)

√2 ⁄ 2

4.

What is the radius of the unit circle?

a)

0

b)

1

c)

1/2

d)

√2/2

5.

What is the value of cosine at 135

a)

0

b)

1/2

c)

√2 /2

d)

-√2 /2

6.

What is the value of sine at 210?

a)

1/2

b)

-1/2

c)

√3 / 2

d)

-√3 / 2

7.

What is the value of cosine at 270

a)

0

b)

1

c)

-1

8.

At what point are sine and cosine the same value?

a)

0

b)

90

c)

45

d)

60

9.

What is the value of sine at 330

a)

1/2

b)

-1/2

c)

√3 / 2

d)

-√3 / 2

10.

What is the value of cosine at 315

a)

0

b)

1

c)

√2 / 2

d)

-√2 /2

11.

What is the value of sine at 150

a)

0

b)

1/2

c)

1

d)

√3 / 2

12.

What is the value of cosine at 0

a)

0

b)

1/2

c)

1

d)

√3 / 2

13.

cos 5π/6

a)

-1/2

b)

1/2

c)

√3/2

d)

-√3/2

14.

cos 4π/3

a)

-√3/2

b)

√3/2

c)

1/2

d)

-1/2

15.

sin 2π/3

a)

1/2

b)

-1/2

c)

√3/2

d)

-√3/2

16.

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)

17.

a)

-√3/2

b)

-½

c)

-√2/2

d)

-1

18.

a)

1

b)

-1

c)

0

d)

√2/2

19.

a)

√3/3

b)

√3

c)

1

d)

undefined

20.

a)

-1

b)

0

c)

undefined

d)

√3

21.

a)

½

b)

√2/2

c)

√3/2

d)

1

22.

sin π/4

a)

√2∕2

b)

1/2

c)

√3/2

d)

0

23.

Find a coterminal angle to 5°.

a)

365°

b)

255°

c)

-220°

d)

-365°

24.

Find a coterminal angle to -90°.

a)

-450°

b)

90°

c)

180°

d)

-180°

25.

In which quadrant is -570⁰

a)

I

b)

II

c)

III

d)

IV

26.

In which quadrant would you find an angle measuring -700°?

a)

1

b)

2

c)

3

d)

4

27.

What are the negative and positive coterminal angles of -225°?

a)

375°, -605°

b)

125°, -355°

c)

135°, -585°

d)

60°, -120°

28.

Find a coterminal angle to -90°.

a)

-450°

b)

90°

c)

180°

d)

-180°

29.

Which of the following is a negative coterminal angle of 165 degrees?

a)

195

b)

525

c)

-525

d)

-195

30.

Which is a coterminal angle to the angle shown?

a)

831

b)

832

c)

833

d)

834

31.

Which is a coterminal angle to the angle shown?

a)

613

b)

73

c)

-117

d)

17

32.

What is the reference angle for 125°?

a)

235°

b)

125°

c)

75°

d)

55°

33.

What is the reference angle for -30°?

a)

150°

b)

30°

c)

80°

d)

60°

34.

What is the reference angle for -310⁰?

a)

50⁰

b)

-50⁰

c)

20⁰

d)

40⁰

35.

What is the reference angle for 275°?

a)

85°

b)

95°

c)

-85°

d)

-95°

36.

What is the reference angle for 63°?

a)

117°

b)

207°

c)

63°

d)

153°

37.

What is the reference angle?

a)

163

b)

73

c)

27

d)

107

38.

Name a quadrant in which ∠A can lie in, if cosA is negative?

a)

2

b)

4

c)

3

d)

1

39.

Name a quadrant in which ∠A can lie in, if tanA is negative?

a)

1

b)

3

c)

2

d)

4

40.

Name a quadrant in which ∠A can lie in, if sinA is negative?

a)

4

b)

3

c)

2

d)

1

41.

Name the quadrant in which ∠A lies, if cosA > 0, sinA < 0

a)

1

b)

2

c)

3

d)

4

42.

Name the quadrant in which ∠A lies, if tanA < 0, cosA < 0

a)

4

b)

3

c)

2

d)

1

43.

Name the quadrant in which ∠A lies, if tanA > 0, sinA < 0

a)

3

b)

4

c)

1

d)

2

44.

Name a quadrant in which ∠A can lie in, if the tanA is positive?

a)

1

b)

2

c)

3

d)

4

45.

How many radians does a circle have?

a)

360 degrees

b)

2pi radians

c)

pi radians

d)

^{2 radians}

46.

Convert π radians to degrees.

a)

90⁰

b)

180⁰

c)

360⁰

d)

60⁰

47.

Convert 150⁰ to radians

a)

5π/6

b)

3π/4

c)

7π/6

d)

2π/3

48.

Convert 100⁰ to radians

a)

5π/9

b)

π/2

c)

5π/8

d)

5π/6

49.

What is 7π/4 radians in degrees?

a)

300

b)

135

c)

315

d)

45

50.

What is 2π/3 radians in degrees?

a)

150

b)

120

c)

180

d)

30

51.

Convert the following to degrees:
-8π/5 radians

a)

-288⁰

b)

-260⁰

c)

-275⁰

52.

Convert the following to radians:
720⁰

a)

3π

b)

4π

c)

5π

53.

a)

27/36

b)

27/45

c)

45/36

d)

45/27

54.

What is the correct ratio?

a)

sin 40 = w/28

b)

cos 40 = w/28

c)

tan 40 = w/28

d)

sin 40 = 28/w

55.

a)

A

b)

B

c)

C

d)

D

56.

a)

A

b)

B

c)

C

d)

D

57.

Which one is the easy way to remember trigonometric ratios?

a)

Sah Coh Toa

b)

Soh Cah Toa

c)

Soh Cah Tao

d)

Soh Ceh Toa

58.

a)

14/48

b)

48/50

c)

14/50

d)

48/14

59.

Choose the correct ratio.

a)

A

b)

B

c)

C

d)

D

60.

Choose the correct ratio.

a)

sin(37)=x/14

b)

cos(37)=x/14

c)

tan(37)=x/14

d)

sin(37)=14/x

61.

What would you use to solve for a?

a)

sin

b)

cos

c)

tan

d)

Pythagorean theorem

62.

Find the length of side w.

a)

21.4 cm

b)

18.0 cm

c)

36.5 cm

d)

43.6 cm

63.

What is the cosine of angle P?

a)

p/q

b)

q/r

c)

p/r

d)

r/q

64.

a)

27/36

b)

27/45

c)

45/36

d)

45/27

65.

a)

A

b)

B

c)

C

d)

D

66.

sin (π/2)

a)

√3/2

b)

√2/2

c)

1/2

d)

1

67.

tan(3π/4)

a)

√2/2

b)

-√2/2

c)

√3/2

d)

-1

68.

cos(2π)

a)

0

b)

1

c)

UND

d)

-1

69.

tan(3π/2)

a)

-1

b)

UND

c)

√2

d)

-√3/3

70.

What is the radius of the unit circle?

a)

0

b)

1

c)

1/2

d)

√2/2

71.

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

a)

y/r

b)

x/r

c)

r/y

d)

y/x

72.

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

a)

y

b)

x

c)

x/y

d)

y/x

73.

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

a)

y

b)

x

c)

x/y

d)

y/x

74.

Choose the best match for the graph.

a)

30^o

b)

45^o

c)

60^o

d)

90^o

75.

Choose the best match for the graph.

a)

30^o

b)

45^o

c)

60^o

d)

90^o

76.

Choose the best match for the graph.

a)

30^o

b)

45^o

c)

60^o

d)

90^o

77.

cos(30^o)

a)

- ½

b)

√3/2

c)

2√3 /3

d)

½

78.

cos(5π/3)

a)

-√2/2

b)

-1/2

c)

1/2

d)

√3/2

79.

cos(π)

a)

√3/2

b)

-√2/2

c)

-1

d)

1

80.

cos (π/4)

a)

√3/2

b)

√2/2

c)

1/2

d)

1

81.

sin (π/2)

a)

√3/2

b)

√2/2

c)

1/2

d)

1

82.

cot(π/4)

a)

- √3/2

b)

-1

c)

-√3

d)

1

83.

csc(11π/6)

a)

-1/2

b)

1/2

c)

-2

d)

-√3/2

84.

sec( $\frac{11\pi}{6}$ )

a)

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

b)

$\frac{1}{2}$

c)

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

d)

-√3

85.

sec(4π/3)

a)

√2/2

b)

-√2/2

c)

√3/2

d)

-2

86.

Find cos( $\frac{10\pi}{3}$ )
hint: find the coterminal angle

a)

(-1/2)

b)

(-√3/2)

c)

(√3/2)

d)

(√2/2)

87.

Find cos(600°)

hint: find the coterminal angle

a)

(-1/2)

b)

(-√3/2)

c)

(√3/2)

d)

(√2/2)

88.

arctan(-1)

a)

3π/2

b)

π/4

c)

-π/4

d)

3π/4 and 7π/4

89.

arccos(-1/2)

a)

π/3

b)

-5π/3

c)

2π/3

d)

2π/3 and 4π/3

90.

arccos(√3/2)

a)

π/6

b)

-π/6

c)

11π/6

d)

π/6 and 11π/6

91.

arcsin(√3/2)

a)

π/3

b)

-π/3

c)

2π/3

d)

π/3 and 2π/3

92.

arctan(-1)

a)

3π/2

b)

π/4

c)

-π/4

d)

3π/4 and 7π/4

93.

What are the domain and range of y = arccos(x)

a)

domain [-1, 1] range [-2π, 2π]

b)

domain [-1, 1] range [0, π]

c)

domain [-1, 1] range [-π/2, π/2]

d)

domain [0, 2π] range [-1, 1]

94.

What are the domain and range of y = arctan(x)

a)

domain [-1, 1] range [-2π, 2π]

b)

domain (-∞, ∞) range [-π/2, π/2]

c)

domain [-1, 1] range (-π/2, π/2)

d)

domain (-∞, ∞) range (-π/2, π/2)

95.

What are the domain and range of y = arcsin(x)

a)

domain [-1, 1] range [-2π, 2π]

b)

domain [-1, 1] range [0, π]

c)

domain [-1, 1] range [-π/2, π/2]

d)

domain [0,2π] range [-1, 1]

96.

Susan is flying a kite, which gets caught in the top of a tree. Use the diagram to estimate the height of the tree.

a)

63 ft

b)

65 ft

c)

74 ft

d)

87 ft

97.

A yacht is anchored 90 feet offshore from the base of a lighthouse. The angle of elevation from the boat to the top of the lighthouse is 26 degrees. The distance between the yacht and the top of the lighthouse is about 100 feet. Which of these is nearest to the height of the lighthouse?

a)

25 feet

b)

45 feet

c)

110 feet

d)

135 feet

98.

What equation can be used to solve for x?

a)

Sin(40°)= x/40

b)

Sin(40º)=x/19

c)

Cos(40º)=x/19

d)

Tan(40°)=19/x

99.

Find x round to the nearest tenth.

a)

46.1

b)

4.9

c)

16.4

d)

26.9

100.

Solve for the misssing distance

a)

18.9

b)

19.5

c)

47

d)

27.5

101.

Find x round to the nearest tenth.

a)

46.1

b)

4.9

c)

16.4

d)

26.9

102.

Solve for x. Round to the nearest tenth.

a)

9.8

b)

0.1

c)

0.038

d)

9.9

103.

Which one is the easy way to remember trigonometric ratios?

a)

Sah Coh Toa

b)

Soh Cah Toa

c)

Soh Cah Tao

d)

Soh Ceh Toa

104.

Find the measurement of the missing side indicated

a)

4.39

b)

3.21

c)

2.19

d)

2.05

105.

Give the Ratio for COS X

a)

Adj/Hyp

b)

Opp/Adj

c)

Adj/Opp

d)

Opp/Hyp

106.

Find the measurement of the missing side indicated

a)

4.39

b)

3.21

c)

2.19

d)

2.05

107.

a)

9/41

b)

40/41

c)

9/40

d)

3/10

108.

What is the value of tan 45⁰?

a)

1/2

b)

0.7071

c)

0.8660

d)

1

109.

Find the length of side w.

a)

21.4 cm

b)

18.0 cm

c)

36.5 cm

d)

43.6 cm

110.

Solve for x. Round to the nearest tenth.

a)

7.5

b)

34.1

c)

14.1

d)

30.1

111.

How do you know which side is the OPPOSITE?

a)

It is next to the right angle

b)

It is opposite the right angle

c)

It is opposite the angle or Theta

d)

It is the bottom leg of the triangle

112.

Choose the correct ratio.

a)

cos(33^o)=x/14

b)

sin(33^o)=x/14

c)

cos(33^o)=14/x

d)

sin(33^o)=14/x

113.

Give the Ratio for SIN X

a)

Opp/Adj

b)

Adj/Hyp

c)

Opp/Hyp

d)

Adj/Opp

114.

a)

14/48

b)

.96

c)

.28

d)

48/14

115.

a)

.75

b)

.6

c)

1.25

d)

45/27

116.

a)

14/48

b)

48/50

c)

14/50

d)

48/14

117.

^{Find the missing side}

a)

11

b)

61

c)

$\sqrt{61}$

d)

$\sqrt{11}$

118.

Which set of sides would make a right triangle?

a)

4,5,6

b)

8,10,12

c)

5,12,13

d)

5,10,12

119.

The Pythagorean Theorem is
a² + b³= c⁴

a)

false

b)

true

120.

The Pythagorean Theorem is
a² + b³= c⁴

a)

false

b)

true

121.

The Pythagorean Theorem ONLY works on which triangle?

a)

obtuse

b)

scalene

c)

isosceles

d)

right

122.

Side a on a right triangle is ALWAYS the longest side.

a)

true

b)

false

123.

How many radians is 250 degrees?

a)

4π/3

b)

25π/18

c)

5π/6

d)

50π/9

124.

Which diagram shows ^3π/₄ ?

a)

b)

c)

d)

125.

On the unit circle, which radian measure represents the point (^√3/₂, -¹/₂)

a)

^11π/₆

b)

^5π/₃

c)

^7π/₆

d)

^4π/₃

126.

How many radians is 216°?

a)

^12π/₅

b)

^6π/₅

c)

^5π/₆

d)

^5π/₉

127.

Which trig functions are positive in the 3rd quadrant?

a)

Sine

b)

Cosine

c)

Tangent

d)

Cosecant

e)

Cotangent

128.

Which of the following are true if

tan Θ = √3 and lies in the first quadrant?

a)

sin Θ = ^√3/₂

b)

sin Θ = ¹/₂

c)

cos Θ = ^√3/₂

d)

cos Θ = ¹/₂

e)

sec Θ = 2

129.

Angle Θ is in Quadrant III with

sin Θ = -³/₅. What is tan Θ?

a)

-¾

b)

-⅗

c)

¾

d)

⅘

130.

Find the exact value of the trig function tan ^7π/₆

a)

^√3/₃

b)

√3

c)

-^√3/₃

d)

^√3/₂

131.

Find tan Θ if cos Θ is -^√3/₂ and

π < Θ < ^3π/₂

a)

tan Θ = ^√3/₃

b)

tan Θ = 1

c)

tan Θ = -^√3/₃

d)

tan Θ = -1

132.

On the unit circle, which radian measure represents the point (^√3/₂, -¹/₂)

a)

^11π/₆

b)

^5π/₃

c)

^7π/₆

d)

^4π/₃

133.

Which of the following are true if

tan Θ = √3 and lies in the first quadrant?

a)

sin Θ = ^√3/₂

b)

sin Θ = ¹/₂

c)

cos Θ = ^√3/₂

d)

cos Θ = ¹/₂

e)

sec Θ = 2

134.

Angle Θ is in Quadrant III with

sin Θ = -³/₅. What is tan Θ?

a)

-¾

b)

-⅗

c)

¾

d)

⅘

135.

Find the exact value of the trig function tan ^7π/₆

a)

^√3/₃

b)

√3

c)

-^√3/₃

d)

^√3/₂

136.

Find tan Θ if cos Θ is -^√3/₂ and

π < Θ < ^3π/₂

a)

tan Θ = ^√3/₃

b)

tan Θ = 1

c)

tan Θ = -^√3/₃

d)

tan Θ = -1

137.

$\cos\left(\theta\right)=?$

a)

$\frac{3}{5}$

b)

$\frac{4}{5}$

c)

$\frac{3}{4}$

d)

$\frac{4}{3}$

138.

$\tan\left(\theta\right)=?$

a)

$\frac{2}{3}$

b)

$\frac{3}{2}$

c)

$\frac{24}{8\sqrt{13}}$

d)

$\frac{16}{8\sqrt{13}}$

139.

$\csc\left(\theta\right)=?$

a)

$\frac{23}{6\sqrt{10}}$

b)

$\frac{23}{13}$

c)

$\frac{6\sqrt{10}}{23}$

d)

$\frac{\sqrt{191}}{13}$

140.

Find the measure of the indicated angle.

a)

$6^{\circ}$

b)

$20^{\circ}$

c)

$43^{\circ}$

d)

$47^{\circ}$

141.

Find the measure of the indicated side.

a)

$15.2$

b)

$11.3$

c)

$11.8$

d)

$13$

142.

In Quadrant I which trig ratios are positive?

a)

All of them

b)

Sine

c)

Tangent

d)

Cosine

143.

In Quadrant II which trig ratios are positive?

a)

All of them

b)

Sine

c)

Tangent

d)

Cosine

144.

In Quadrant III which trig ratios are positive?

a)

All of them

b)

Sine

c)

Tangent

d)

Cosine

145.

In Quadrant IV which trig ratios are positive?

a)

All of them

b)

Sine

c)

Tangent

d)

Cosine

146.

When creating a triangle from a terminal side of an angle the x value is...

a)

the adjacent side length

b)

the opposite side length

c)

the hypotenuse

147.

When creating a triangle from a terminal side of an angle the y value is...

a)

the adjacent side length

b)

the opposite side length

c)

the hypotenuse

148.

The hypotenuse of a triangle on our coordinate grid is always..

a)

positive

b)

negative

c)

havin a good time

149.

what is the formula for finding the hypotnuse?

a)

a²⁺b²=c²

b)

a+b=c

c)

a-b=c

d)

c-a=c

150.

Choose the correct ratio.

a)

cos(33)=x/14

b)

sin(33)=x/14

c)

cos(33)=14/x

d)

sin(33)=14/x

151.

Which one is the easy way to remember trigonometric ratios?

a)

Sah Coh Toa

b)

Soh Cah Toa

c)

Soh Cah Tao

d)

Soh Ceh Toa

152.

$\frac{10\pi}{9}$ What quadrant is the measurement to the left in?

a)

I

b)

II

c)

III

d)

IV

153.

$-\frac{5\pi}{3}$ What quadrant is the measurement to the left in?

a)

I

b)

II

c)

III

d)

IV

154.

What is the value of "x" in the diagram below?

a)

2.5

b)

5

c)

5√3

d)

10

155.

Name a quadrant in which ∠A can lie in, if cosA is negative?

a)

2

b)

4

c)

3

d)

1

156.

Name a quadrant in which ∠A can lie in, if the sinA is positive?

a)

1

b)

2

c)

3

d)

4

157.

Name a quadrant in which ∠A can lie in, if cosA is negative?

a)

2

b)

4

c)

3

d)

1

158.

Name a quadrant in which ∠A can lie in, if tanA is negative?

a)

1

b)

3

c)

2

d)

4

159.

Name a quadrant in which ∠A can lie in, if sinA is negative?

a)

4

b)

3

c)

2

d)

1

160.

Name the quadrant in which ∠A lies, if cosA > 0, sinA < 0

a)

1

b)

2

c)

3

d)

4

161.

Name the quadrant in which ∠A lies, if tanA < 0, cosA < 0

a)

4

b)

3

c)

2

d)

1

162.

Name the quadrant in which ∠A lies, if tanA > 0, sinA < 0

a)

3

b)

4

c)

1

d)

2

163.

Name a quadrant in which ∠A can lie in, if the tanA is positive?

a)

1

b)

2

c)

3

d)

4

Intro to Trig

Total questions: 163

Worksheet time: 8hrs 13mins

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