Free Printable Unit 7 Basic Trig and the Unit Circle

1.

Convert 510^o to Radians

a)

25π / 3

b)

23π / 8

c)

17π / 6

d)

51π / 8

2.

Convert 150⁰ to Radians

a)

5π/6

b)

3π/4

c)

7π/6

d)

2π/3

3.

Convert -520^o into Radians

a)

-17π / 4

b)

-21π / 6

c)

-26π / 9

d)

-23π / 6

4.

Convert -40^o into Radians

a)

-4π / 8

b)

-8π / 9

c)

-2π / 9

d)

-5π / 8

5.

Convert 35π / 18 radians into degrees

a)

350^o

b)

340^o

c)

355^o

d)

345⁰

6.

Convert -41π / 12 radians into degrees

a)

-600^o

b)

-605^o

c)

-610^o

d)

-615^o

7.

Convert 7π/ 6 radians into degrees

a)

225

b)

210

c)

270

d)

240

8.

Convert π radians to degrees.

a)

90⁰

b)

180⁰

c)

360⁰

d)

60⁰

9.

Convert π/3 radians to degrees

a)

60⁰

b)

30⁰

c)

90⁰

d)

45⁰

10.

Convert π/4 radians to degrees

a)

90⁰

b)

45⁰

c)

60⁰

d)

30⁰

11.

What is 2π/3 radians in degrees?

a)

150

b)

120

c)

180

d)

30

12.

What is 90 degrees in radians?

a)

π/4

b)

π/2

c)

π/6

d)

3π/2

13.

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

a)

375°, -600°

b)

125°, -356°

c)

135°, -585°

d)

60°, -120°

14.

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

a)

195

b)

525

c)

-525

d)

-195

15.

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

a)

540°, -120°

b)

600°, -120°

c)

425°, -240°

d)

120°, -135°

16.

Find a coterminal angle to 0 degrees.

a)

360

b)

180

c)

90

d)

270

17.

Find a coterminal angle to -180 degrees.

a)

180

b)

90

c)

270

d)

360

18.

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

a)

-165

b)

525

c)

-525

d)

-555

19.

What is 360 degrees in radians?

a)

2π/3

b)

5π/4

c)

2π

d)

π

20.

What is 45 degrees in radians?

a)

π/2

b)

π/6

c)

π/4

d)

3π/4

21.

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

22.

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°

23.

A ceiling fan with 16 inch blades rotates at 45 rpm. Find the angular velocity of the fan in rad/min. Round to the nearest tenth.

a)

90 rad/min

b)

282.7 rad/min

c)

45 rad/min

d)

141.4

24.

Determine the linear velocity of the tips of the blades in inches per minute for a ceiling fan with 20 inch blades rotating at 45 rpm.

a)

5654.9 in/min

b)

1800 in/min

c)

2827.4 in/min

d)

900 in/min

25.

How many revolutions will a car wheel of diameter 30 in. make as the car travels a distance of one mile? (Hint: determine the circumference first ... rev/circumference ... then convert to rev/mile) Round answer to the nearest tenth.

a)

6635.0 rev/mile

b)

672.3 rev/mile

c)

884.7 rev/mile

26.

The wheels of a car have radius 11 in. and are rotating at 600 rpm. Determine the speed of the car in miles/hour to the nearest tenth. (Determine ω (angular velocity) first and then use v=ω⋅r and convert to miles/hour)

a)

6.3 miles/hour

b)

12.5 miles/hour

c)

39.3 miles/hour

d)

78.5 miles/hour

27.

Determine the angular velocity in rad/min of a gyroscope rotating at 6 rps (revolutions per second). Leave answer in terms of π.

a)

360π rad/min

b)

12π rad/min

c)

360 rad/min

d)

720π rad/min

28.

A gear spins at a rate of 400 revolutions/minute. Which choice is closest to its angular speed in radians/second?

a)

6.67 rad/s

b)

2500 rad/s

c)

41.9 rad/s

d)

20.9 rad/s

29.

A record spins at 33 rpm (revolutions per minute), which is an angular speed of about 3.46 radians per second. What is the approximate linear speed of a fly that sits on the record, 12 cm from the center?

a)

3.4 cm/s

b)

21.5 cm/s

c)

41.5 cm/s

d)

131.9 cm/s

30.

A child sits 0.75 m from the center of a merry go round. The merry go round makes one revolutions in 4 seconds. What is the child's linear speed? (Use 3.14 as pi, and Round your answer to tenths)

a)

1.9 m/s

b)

1.2 m/s

c)

12.6 m/s

d)

4.71 m/s

31.

The wheel of a machine rotates at the rate of 300 rpm (revolutions per minute). If the diameter of the wheel is 80 cm, what is the angular speed in radian per second ?

a)

1884.96 rad/sec

b)

24,000 rad/sec

c)

31.42 rad/sec

d)

1256.29 rad/sec

32.

The wheel of a machine rotates at the rate of 300 rpm (rotation per minute). If the diameter of the wheel is 80 cm, what is the linear speed (in cm per second) of a point on the wheel?

a)

1257 cm/sec

b)

200 cm/sec

c)

1440,000 cm/sec

d)

542 cm/sec

33.

Find the arc length.

a)

3π/4 ft

b)

39π/4 ft

c)

13π/4 ft

d)

4π/13 ft

34.

A ceiling fan has 18 inch blades and turns at a rate of 45 revolutions per minute. What is the angular speed in radians per hour?

a)

90π rad / 1 hr

b)

2700π rad / 1 hr

c)

5400π rad / 1 hr

d)

97200π rad / 1 hr

35.

A car tire has a diameter of 14 inches and is spinning at 10 revolutions per second. What is the linear speed in miles per hour?

a)

7.95π mi / 1 hr

b)

15.90 mi / 1 hr

c)

3.28 rad / 1 hr

d)

2.84 rad / 1 hr

36.

A car tire has a diameter of 14 inches and is spinning at a rate of 10 revolutions per second. What is the angular speed in radians per hour?

a)

120π rad / 1 hr

b)

1,008,000π rad / 1 hr

c)

504,000π rad / 1 hr

d)

7200π rad / 1 hr

37.

A spin balancer rotates the wheel of a car at 500 revolutions per minute. If the diameter of the wheel is 26 inches, what road speed is being tested?

a)

12.31π mi / 1 hr

b)

12.09π mi / 1 hr

c)

13. 44π mi / 1 hr

d)

24.62π mi / 1 hr

38.

A grindstone spinning at the rate of 8.3 rev/s has what approximate angular speed?

a)

3.2 rad/s

b)

26 rad/s

c)

52 rad/s

d)

81 rad/s

39.

Two bugs ride a turntable which is rotating at a constant rate of 4 rad/s. Bug A is at a radius of 4 cm, while bug B is at a radius of 8 cm. Which of the following is true?

a)

Bug A has a greater rotational speed.

b)

Bug B has a greater rotational speed.

c)

Bug A has a greater speed.

d)

Bug B has a greater speed.

40.

Which has greater angular speed, a horse near the outside rail of a merry-go-round or a horse near the inside rail?

a)

The inside horse

b)

The outside horse

c)

Neither - they both have the same angular speed

41.

A bug on a turning phonograph record will make more turns per minute if it is located toward the center of the record.

a)

True

b)

False

42.

Name the quadrant the point is in:

\left(-13,\ 2\right)

a)

1

b)

2

c)

I

d)

II

e)

IV

43.

Find the value of tan $\theta$ given the point

\left(8,\ -\sqrt{17}\right)

a)

$-\frac{9\sqrt{17}}{17}$

b)

$\frac{9\sqrt{130}}{130}$

c)

$-\frac{8\sqrt{17}}{17}$

d)

$-\frac{\sqrt{17}}{8}$

44.

Find the value of sin $\theta$ given the point

\left(2,\ -\sqrt{5}\right)

a)

$-\frac{\sqrt{10}}{3}$

b)

$-\frac{3\sqrt{10}}{10}$

c)

$\frac{\sqrt{10}}{10}$

d)

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

45.

Find the value of cos $\theta$ given the point

\left(5,\ \sqrt{11}\right)

a)

$\frac{6\sqrt{11}}{11}$

b)

$\frac{6}{5}$

c)

$\frac{\sqrt{11}}{5}$

d)

$\frac{5}{6}$

46.

Find the value of sec $\theta$ given the point

\left(-\sqrt{7},\ 3\right)

a)

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

b)

$\frac{3}{4}$

c)

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

d)

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

47.

Find the value of cot $\theta$ given the point

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

a)

$-\sqrt{3}$

b)

$\frac{3\sqrt{73}}{73}$

c)

$-\frac{3}{8}$

d)

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

48.

Find the value of csc $\theta$ given the point

\left(-\sqrt{17},\ 8\right)

a)

$-\frac{\sqrt{17}}{8}$

b)

$\frac{9}{8}$

c)

$-\frac{8\sqrt{17}}{17}$

d)

$-\frac{9\sqrt{17}}{17}$

49.

Find the value of sec $\theta$ given the point

\left(-9,\ -\sqrt{19}\right)

a)

$\frac{\sqrt{19}}{9}$

b)

$-\frac{10\sqrt{19}}{19}$

c)

$-\frac{9}{10}$

d)

$-\frac{10}{9}$

50.

Find the value of sin $\theta$ given the point

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

a)

$-\sqrt{3}$

b)

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

c)

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

d)

$\frac{1}{2}$

51.

Find the value of csc $\theta$ given the point

\left(4,\ 3\right)

a)

$\frac{5}{4}$

b)

$\frac{3}{5}$

c)

$\frac{4}{5}$

d)

$\frac{5}{3}$

52.

Find the value of cot $\theta$ given the point

\left(13,\ 2\right)

a)

$\frac{2}{13}$

b)

$\frac{13}{2}$

c)

$\frac{\sqrt{173}}{2}$

d)

$\frac{13\sqrt{173}}{173}$

53.

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

54.

The hypotenuse of any right triangle from the center of the unit circle to an edge is always

a)

1

b)

√2 / 2

c)

√3 / 2

d)

1/2

55.

If you are given the two sides that are not the hypotenuse, which trig function should you use?

a)

sine

b)

cosine

c)

tangent

d)

inverse

56.

If you are given the hypotenuse and an adjacent side, which trig function should you use?

a)

sine

b)

cosine

c)

tangent

d)

inverse

57.

Which of these points is NOT on the unit circle?

a)

(1,0)

b)

(0,1)

c)

(-1,0)

d)

(0,0)

58.

Is the point (½, ½) on the unit circle?

a)

Yes

b)

No

c)

How am I supposed to know?

d)

I'll tell you next class.

59.

What's the angle measure to the point (½ , √3 ∕ 2) ?

a)

30°

b)

45°

c)

60°

d)

90°

60.

What's the angle measure to the point (√3 ∕ 2, ½) ?

a)

30°

b)

45°

c)

60°

d)

90°

61.

What's the point on the circle at 45° ?

a)

(√2 /2 , √2 /2)

b)

(-√2 /2 , √2 /2)

c)

(-√2 /2 , -√2 /2)

d)

(√2 /2 , -√2 /2)

62.

What's the point on the circle at 135° ?

a)

(√2 /2 , √2 /2)

b)

(-√2 /2 , √2 /2)

c)

(-√2 /2 , -√2 /2)

d)

(√2 /2 , -√2 /2)

63.

cos(90^o)=

a)

1

b)

0

c)

-1

d)

½

64.

sin(90^o)=

a)

1

b)

0

c)

-1

d)

½

65.

Choose the correct ratio.

a)

sin(37)=x/14

b)

cos(37)=x/14

c)

tan(37)=x/14

d)

sin(37)=14/x

66.

Find the length of side w.

a)

21.4 cm

b)

18.0 cm

c)

36.5 cm

d)

43.6 cm

67.

Find x round to the nearest tenth.

a)

46.1

b)

4.9

c)

16.4

d)

26.9

68.

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)

69.

What is the reference angle for 125°?

a)

235°

b)

125°

c)

75°

d)

55°

70.

What is the reference angle for -30°?

a)

150°

b)

30°

c)

80°

d)

60°

71.

What is the reference angle for -310⁰?

a)

50⁰

b)

-50⁰

c)

20⁰

d)

40⁰

72.

What is the reference angle for 275°?

a)

85°

b)

95°

c)

-85°

d)

-95°

73.

What is the reference angle for 63°?

a)

117°

b)

207°

c)

63°

d)

153°

74.

What is the reference angle?

a)

163

b)

73

c)

27

d)

107

75.

What is the reference angle?

a)

43

b)

-43

c)

47

d)

-47

76.

What is the reference angle?

a)

112

b)

68

c)

158

d)

248

77.

What is the reference angle?

a)

7

b)

63

c)

277

d)

97

78.

What is the reference angle?

a)

48

b)

138

c)

132

d)

42

79.

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)

$-\frac{3}{4}$

80.

$\tan\ 300\degree$ = ______

a)

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

b)

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

c)

$\sqrt{3}$

d)

$-\sqrt{3}$

81.

\sin225\degree

=_______

a)

$\frac{1}{2}$

b)

$-\frac{1}{2}$

c)

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

d)

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

82.

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

a)

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

b)

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

c)

$\frac{1}{2}$

d)

$-\frac{1}{2}$

83.

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

a)

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

b)

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

c)

$\frac{1}{2}$

d)

$-\frac{1}{2}$

84.

\cos315\degree

= ______

a)

$\frac{1}{2}$

b)

$-\frac{1}{2}$

c)

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

d)

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

85.

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

a)

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

b)

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

c)

$\sqrt{3}$

d)

$-\sqrt{3}$

86.

\sin90\degree

= ______

a)

0

b)

1

c)

-1

d)

does not exist

87.

a)

A

b)

B

c)

C

d)

D

88.

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)

89.

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

90.

Using reference angles find csc 330^o.

a)

-2

b)

2

c)

1

d)

-1

91.

What is the reference angle for 2pi/3

a)

pi/4

b)

7pi/6

c)

4pi/3

d)

pi/3

92.

a)

π/2

b)

π/3

c)

π/4

d)

π/6

93.

How many radians does a circle have?

a)

360 degrees

b)

2pi radians

c)

pi radians

d)

^{2 radians}

94.

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.

95.

Find the reference angle.

a)

$-\frac{4\pi}{9}$

b)

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

c)

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

d)

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

96.

Find the reference angle.

a)

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

b)

$\frac{\pi}{4}$

c)

$\frac{3\pi}{8}$

d)

$-\frac{3\pi}{8}$

97.

Find the exact value of the trig function.

a)

-1

b)

1

c)

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

d)

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

98.

Find the exact value of the trig function.

a)

0

b)

1

c)

-1

d)

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

99.

Find the exact value of the trig function.

a)

0

b)

1

c)

-1

100.

The cosecant function is equivalent to...(check all that apply)

a)

$\frac{1}{\cos x}$

b)

$\frac{1}{\sin x}$

c)

Positive in quadrants I and II

d)

Positive in quadrants I and IV

e)

$\frac{\sin x}{\cos x}$

101.

Of the following, which trig ratio can never be greater than 1?

a)

sine

b)

secant

c)

tangent

d)

cosecant

102.

A straight angle is _____ radians.

a)

$\frac{\pi}{2}$

b)

$\pi$

c)

$2\pi$

d)

$4\pi$

103.

A full rotation is _____ radians.

a)

$\frac{\pi}{2}$

b)

$\pi$

c)

$2\pi$

d)

$4\pi$

104.

$Find\ the\ reference\ angle\ for\ \theta=2.5$

a)

-.64

b)

.64

c)

$\pi$

d)

5.64

105.

$Find\ the\ reference\ angle\ for\ \theta=-5.25$

a)

1.03

b)

2.11

c)

$\frac{\pi}{4}$

d)

8.39

106.

$Find\ an\ angle\ \cot er\min al\ to\ \ \theta=-1.25$

a)

5.03

b)

1.89

c)

$-4.39$

d)

9

Unit 7 Basic Trig and the Unit Circle

Total questions: 106

Worksheet time: 9hrs 50mins

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