Free Printable Trig and the Unit Circle

1.

sin π/4

a)

√2∕2

b)

1/2

c)

√3/2

d)

0

2.

Tangent is...

a)

a. Opposite/hypotenuse

b)

b. sine/cosine

c)

c. neither a or b

d)

d. both a and b

3.

sin π/4

a)

√2∕2

b)

1/2

c)

√3/2

d)

0

4.

cos 5π/6

a)

-1/2

b)

1/2

c)

√3/2

d)

-√3/2

5.

tan 7π/4

a)

-1

b)

1

c)

√2/2

d)

undefined

6.

cos 4π/3

a)

-√3/2

b)

√3/2

c)

1/2

d)

-1/2

7.

cot π/2

a)

undefined

b)

0

c)

1

d)

1/2

8.

tan (-π)

a)

undefined

b)

0

c)

1

d)

-1

9.

What is the radius of the unit circle?

a)

0

b)

1

c)

1/2

d)

√2/2

10.

What is the value of cosine at 0

a)

0

b)

1/2

c)

1

d)

√3 / 2

11.

sin 0

a)

0

b)

1

c)

-1

d)

und

12.

sec π

a)

1

b)

-1

c)

0

d)

und

13.

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)

14.

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

15.

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

16.

Who's logo is this?

a)

McDonalds

b)

Burger King

c)

Checkers

d)

Wendys

17.

Sine is even

a)

True

b)

False

18.

The period of the tangent function is

a)

$\frac{\pi}{2}$

b)

$2\pi$

c)

$\pi$

d)

3

19.

The period of the secant function is

a)

$\frac{\pi}{4}$

b)

$\pi$

c)

$\frac{\pi}{2}$

d)

$2\pi$

20.

What are the coordinates of 60° on the unit circle?

a)

(0, 1)

b)

(1/2, √3/2)

c)

(√3/2, 1/2)

d)

(√2/2, 1/2)

21.

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

22.

Given the ordered pair (-¹/₂ , ^√3/₂), what is the value of cosine?

a)

√3

b)

^-1/₂

c)

^√3/₂

d)

^√3/₃

23.

Evaluate sin (7π/6).

a)

1/2

b)

-1/2

c)

√3/2

d)

-√3/2

24.

Evaluate cos (150^o).

a)

-1/2

b)

1/2

c)

√3/2

d)

-√3/2

25.

Find θ if tan θ = -1, and θ is in Quadrant II

a)

2π/3

b)

5π/6

c)

3π/4

d)

5π/4

26.

Find θ if $\sin\left(\theta\right)=-\frac{\sqrt{3}}{2}$ , and θ is in Quadrant III.

a)

4π/3

b)

7π/6

c)

3π/4

d)

5π/4

27.

For an angle $\theta$ in standard position and a point (7, -24) on the terminal side, find $\sin\theta$ .

a)

$-\frac{24}{25}$

b)

$\frac{7}{25}$

c)

$-\frac{24}{7}$

d)

$-\frac{7}{24}$

28.

For an angle $\theta$ in standard position and a point (7, -24) on the terminal side, find $\cos\theta$ .

a)

$-\frac{24}{25}$

b)

$\frac{7}{25}$

c)

$-\frac{24}{7}$

d)

$-\frac{7}{24}$

29.

For an angle $\theta$ in standard position and a point (7, -24) on the terminal side, find $\tan\theta$ .

a)

$-\frac{24}{25}$

b)

$\frac{7}{25}$

c)

$-\frac{24}{7}$

d)

$-\frac{7}{24}$

30.

Find $\cos\theta$ for an angle in standard position that passes through the point

\left(-1,\ \sqrt{3}\right)

a)

$-\frac{1}{2}$

b)

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

c)

$-2$

d)

$\frac{1}{2}$

31.

Find $\sin\theta$ for an angle in standard position that passes through the point

\left(-1,\ \sqrt{3}\right)

.

a)

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

b)

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

c)

$-2$

d)

$\frac{1}{2}$

32.

In which quadrant does $\theta=30\degree$ lie?

a)

Quadrant I

b)

Quadrant II

c)

Quadrant III

d)

Quadrant IV

33.

In which quadrant does $\theta=210\degree$ lie?

a)

Quadrant I

b)

Quadrant II

c)

Quadrant III

d)

Quadrant IV

34.

In which quadrant does $\theta=\frac{3\pi}{4}$ lie?

a)

Quadrant I

b)

Quadrant II

c)

Quadrant III

d)

Quadrant IV

35.

In which quadrant does $\theta=\frac{11\pi}{6}$ lie?

a)

Quadrant I

b)

Quadrant II

c)

Quadrant III

d)

Quadrant IV

36.

What ordered pair is associated with $\theta=\frac{5\pi}{3}$

a)

$\left(\frac{\sqrt{3}}{2},\ -\frac{1}{2}\right)$

b)

$\left(\frac{1}{2},\ \frac{\sqrt{3}}{2}\right)$

c)

$\left(-\frac{1}{2},\ \frac{\sqrt{3}}{2}\right)$

d)

$\left(\frac{1}{2},\ -\frac{\sqrt{3}}{2}\right)$

37.

Evaluate $\sin\left(210\degree\right)$

a)

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

b)

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

c)

$-\frac{1}{2}$

d)

$\frac{1}{2}$

38.

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

a)

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

b)

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

c)

$-\frac{1}{2}$

d)

$\frac{1}{2}$

39.

Evaluate $\sin\left(240\degree\right)$

a)

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

b)

$-\frac{1}{2}$

c)

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

d)

$\frac{1}{2}$

40.

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 theta

d)

It is the bottom leg of the triangle

41.

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

42.

Solve for x.

a)

24.20

b)

4.92

c)

290.4

d)

29.75

43.

What is the radius of a unit circle?

a)

1

b)

2

c)

1/2

d)

0

44.

Give the Ratio for SIN X

a)

opp/adj

b)

Adj/hyp

c)

Opp/hyp

d)

adj/opp

45.

Give the Ratio for COS X

a)

Adj/Hyp

b)

Opp/Adj

c)

Adj/Opp

d)

Opp/Hyp

46.

What is
cos 90^o?

a)

1

b)

0

c)

-1

d)

1/2

47.

Convert π radians to degrees.

a)

90⁰

b)

180⁰

c)

360⁰

d)

60⁰

48.

Convert π/3 radians to degrees

a)

60⁰

b)

30⁰

c)

90⁰

d)

45⁰

49.

A triangle has two equal sides only. What is it called?

a)

Scalene

b)

Isoceles

c)

Right-angled

d)

Equilateral

50.

An angle is 135°. What is it called?

a)

A straight angle

b)

An acute angle

c)

A reflex angle

d)

An obtuse angle

51.

Tangent is...

a)

a. Opposite/Adjacent

b)

b. Opposite/Hypotenuse

c)

c. neither a or b

d)

d. both a and b

52.

^{1/Tan x =}

a)

cos x

b)

csc x

c)

sec x

d)

cot x

53.

Find the missing side u

a)

2√3

b)

4

c)

8

d)

4√3

54.

Find the measurement of the missing side indicated

a)

4.39

b)

3.21

c)

2.19

d)

2.05

55.

Find the missing angle indicated by
θ

a)

21.80

b)

23.57

c)

66.4

d)

69.8

56.

A 14 foot ladder is used to scale a 13 foot wall. At what angle of elevation must the ladder be situated in order to reach the top of the wall?

a)

68.2

b)

21.79

c)

42.87

d)

162.5

57.

Solve for the misssing distance

a)

18.9

b)

19.5

c)

47

d)

27.5

58.

What are the two angles between 0 and 360 degrees that correspond to a sine value of 0.5?

a)

210° and 30°

b)

150° and 210°

c)

210° and 330°

d)

150° and 30°

59.

What are the two angles between 0 and 360 degrees that correspond to a tan value of 1.6?

a)

57.99 and 237.99

b)

57.99 and 212.01

c)

56.25 and 212.01

d)

56.25 and 237.99

60.

Choose the best match for the graph.

a)

30^o

b)

45^o

c)

60^o

d)

90^o

61.

Choose the best match for the graph.

a)

30^o

b)

45^o

c)

60^o

d)

90^o

62.

Choose the best match for the graph.

a)

30^o

b)

45^o

c)

60^o

d)

90^o

63.

Choose the best match for the graph.

a)

45^o

b)

90^o

c)

135^o

d)

180^o

64.

a)

csc x

b)

sec x

c)

cot x

d)

tan x

65.

tan 2π =

a)

0

b)

1

c)

-1

d)

undefined

66.

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

67.

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

68.

tanθ 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

69.

sin π =

a)

0

b)

1

c)

-1

d)

undefined

70.

cos π =

a)

0

b)

1

c)

-1

d)

undefined

71.

What is the measure of the given angle?

a)

-110 degrees

b)

70 degrees

c)

110 degrees

d)

-70 degrees

72.

What is the measure of the given angle?

a)

-940 degrees

b)

140 degrees

c)

-40 degrees

d)

240 degrees

73.

What is the measure of the given angle?

a)

8pi/3

b)

5pi/6

c)

-2pi/3

d)

-pi/6

74.

What is the measure of the given angle?

a)

17pi/4

b)

9pi/4

c)

-pi/4

d)

-7pi/4

75.

Which trig equation is correct based on the diagram?

a)

b)

c)

d)

e)

The correct answer is not listed

76.

Which trig equation is correct based on the diagram?

a)

b)

c)

d)

e)

The correct answer is not listed

77.

Using the Unit Circle, find the exact value of this trig function.

a)

b)

c)

d)

e)

The correct answer is not listed

78.

Using the Unit Circle, find the exact value of this trig function.

a)

1

b)

0

c)

-1

d)

undefined

e)

The correct answer is not listed

79.

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

a)

y/r

b)

x/r

c)

r/y

d)

y/x

80.

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

a)

y

b)

x

c)

x/y

d)

y/x

81.

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

a)

y

b)

x

c)

x/y

d)

y/x

82.

Choose the best match for the graph.

a)

45^o

b)

90^o

c)

135^o

d)

180^o

83.

Choose the best match for the graph.

a)

30^o

b)

45^o

c)

60^o

d)

90^o

84.

Choose the best match for the graph.

a)

30^o

b)

45^o

c)

60^o

d)

90^o

85.

Choose the best match for the graph.

a)

30^o

b)

45^o

c)

60^o

d)

90^o

86.

a)

b)

c)

d)

87.

Which is a coterminal angle for 435 degrees?

a)

-195 degrees

b)

-105 degrees

c)

-285 degrees

d)

-15 degrees

88.

Which is a coterminal angle for the given angle?

\frac{19\pi}{9}

a)

$\frac{11\pi}{18}$

b)

$\frac{10\pi}{9}$

c)

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

d)

$\frac{\pi}{9}$

89.

Evaluate.

\sin315\degree

a)

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

b)

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

c)

$-\sqrt{2}$

d)

$-\frac{1}{2}$

90.

Evaluate

\cos\frac{2\pi}{3}

a)

1

b)

$\sqrt{2}$

c)

$-\frac{1}{2}$

d)

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

91.

Evaluate

\csc210\degree

a)

$-\sqrt{2}$

b)

-2

c)

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

d)

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

92.

Evaluate

\sec\frac{\pi}{6}

a)

0

b)

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

c)

$\sqrt{3}$

d)

Undefined

93.

Evaluate

\tan300\degree

a)

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

b)

$-\sqrt{3}$

c)

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

d)

$\sqrt{3}$

94.

Evaluate

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

a)

Undefined

b)

2

c)

$\frac{1}{2}$

d)

0

95.

Find the reference angle for:

290\degree

a)

20 degrees

b)

70 degrees

c)

110 degrees

d)

470 degrees

96.

Convert the radian measure into degrees:

a)

110 degrees

b)

100 degrees

c)

95 degrees

d)

120 degrees

97.

Find Sin Ɵ

a)

5/13

b)

5/12

c)

13/5

d)

13/12

98.

Find Tan Ɵ

a)

5/13

b)

5/12

c)

13/5

d)

13/12

99.

Find Sec Ɵ

a)

5/13

b)

5/12

c)

13/5

d)

13/12

100.

Find Csc Ɵ

a)

$\frac{2\sqrt{21}}{21}$

b)

$\frac{5}{2}$

c)

$\frac{\sqrt{21}}{2}$

d)

$\frac{\sqrt{21}}{5}$

101.

Find Cot Ɵ

a)

$\frac{2\sqrt{21}}{21}$

b)

$\frac{5}{2}$

c)

$\frac{\sqrt{21}}{2}$

d)

$\frac{\sqrt{21}}{5}$

102.

Find Sec Ɵ

a)

$\frac{2\sqrt{21}}{21}$

b)

$\frac{5}{2}$

c)

$\frac{3\sqrt{21}}{21}$

d)

$\frac{5\sqrt{21}}{21}$

103.

If Sec Ø = 25/24, then find Tan Ø =

a)

24/25

b)

7/25

c)

24/7

d)

7/24

104.

If Cos Ø = 3/5, then find Csc Ø =

a)

5/3

b)

4/5

c)

5/4

d)

4/3

105.

Convert 173.459º to Degrees, Minutes, Seconds

a)

173º 27' 32.4"

b)

173º 27' 324"

c)

173º 32' 27"

d)

173º 324' 27"

106.

Convert -208.45º to Degrees Minutes Seconds

a)

208º 27"

b)

-208º 27"

c)

-208º 27'

d)

208º 27'

107.

Convert 163º 24' 28" to Degrees

a)

163.4567º

b)

163.5789º

c)

163.2091º

d)

163.4078º

108.

Convert 309º 42" to Degrees

a)

309.6789º

b)

309.0117º

c)

309.5566º

d)

309.7245º

109.

What is the radian equivalent of 210 degrees?

a)

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

b)

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

c)

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

d)

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

110.

What is the radian equivalent of -460 degrees?

a)

$\frac{9\pi}{23}$

b)

$\frac{23\pi}{9}$

c)

$-\frac{23\pi}{9}$

d)

$-\frac{9\pi}{23}$

111.

Which of the following is equivalent to $89^o11'15"$ ?

a)

89.5 degrees

b)

89.4 degrees

c)

89.1 degrees

d)

89.2 degrees

112.

\frac{5\pi}{6}

a)

140

b)

150

c)

210

d)

216

113.

What is the equivalent degree measure of $\frac{4\pi}{3}$

a)

150

b)

240

c)

270

d)

300

114.

Which angle is coterminal to 480 degrees?

a)

-480 degrees

b)

60 degrees

c)

120 degrees

d)

280 degrees

115.

What is the equivalent radian measure of 230 degrees?

a)

$\frac{5\pi}{18}$

b)

$-\frac{5\pi}{18}$

c)

$\frac{23\pi}{18}$

d)

$-\frac{23\pi}{18}$

116.

What is the equivalent degree measure for $\frac{5\pi}{12}$ ?

a)

75 degrees

b)

150 degrees

c)

-75 degrees

d)

220 degrees

117.

Which angle is coterminal to $-\frac{5\pi}{3}$ ?

a)

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

b)

$\frac{\pi}{6}$

c)

$\frac{\pi}{3}$

d)

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

118.

What is the radian equivalent of -240 degrees?

a)

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

b)

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

c)

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

d)

$\frac{\pi}{3}$

119.

Calculate the length of an arc with radius 15 cm and central angle of 30°.

a)

450 cm

b)

5π/2 cm or ≈ 7.9 cm

c)

225 cm

d)

5π/4 cm or ≈ 3.9 cm

120.

Determine the central angle if the arc length is 10 cm and the radius is 5 cm.

a)

2°

b)

not possible ... "s" is too small

c)

≈ 114.6°

d)

360°

121.

A merry go round makes 18 rotations in 2 minutes. What is its angular speed in rpm?

a)

3 rpm

b)

6 rpm

c)

9rpm

d)

12 rpm

122.

A girl sits 2.0 meters (m) from the center of a merry go round. How far does she travel during one revolution? Use 3.14 as pi.

a)

540 degrees

b)

12.6 m

c)

9.42 m

d)

360 degrees

Trig and the Unit Circle

Total questions: 122

Worksheet time: 3hrs 5mins

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