Free Printable 6.6 -6.10 Review - Unit Circle, Circular Motion, Radians (PC)

1.

Find:

\sin\frac{\pi}{4}

a)

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

b)

$\frac{1}{2}$

c)

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

d)

$0$

2.

Find:

\cos\frac{5\pi}{6}

a)

$-\frac{1}{2}$

b)

$\frac{1}{2}$

c)

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

d)

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

3.

Find:

\tan\frac{7\pi}{4}

a)

$-1$

b)

$1$

c)

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

d)

undefined

4.

Find:

\cos\ \frac{4\pi}{3}

a)

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

b)

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

c)

$\frac{1}{2}$

d)

$-\frac{1}{2}$

5.

Find:

\cot\ \frac{3\pi}{4}

a)

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

b)

$-1$

c)

$1$

d)

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

6.

Find:

\sin\ \frac{7\pi}{6}

a)

$\frac{1}{2}$

b)

$-\frac{1}{2}$

c)

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

d)

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

7.

Find:

\tan\ \left(-\pi\right)

a)

undefined

b)

0

c)

1

d)

-1

8.

For what angles are sine and cosine the same?

a)

0^o

b)

45^oand 135⁰

c)

45^oand 225⁰

d)

45^oand 315⁰

9.

\frac{4\pi}{3}

is equal to how many degrees?

a)

60°

b)

240°

c)

300°

d)

120°

10.

$\frac{\pi}{2}$ is equal to how many degrees?

a)

180°

b)

90°

c)

135°

d)

240°

11.

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

a)

(0, 1)

b)

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

c)

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

d)

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

12.

What the coordinates of 270° on the unit circle?

a)

$\left(0,1\right)$

b)

$\left(1,\ 0\right)$

c)

$\left(-1,\ 0\right)$

d)

$\left(0,\ -1\right)$

13.

90° is equal to how many radians?

a)

$\frac{\pi}{4}$

b)

$\frac{\pi}{2}$

c)

$\pi$

d)

$2\pi$

14.

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

a)

y

b)

$\frac{x}{y}$

c)

$\frac{1}{y}$

d)

$\frac{y}{x}$

15.

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

a)

y

b)

x

c)

$\frac{1}{y}$

d)

$\frac{y}{x}$

16.

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

a)

y

b)

x

c)

$\frac{1}{y}$

d)

$\frac{y}{x}$

17.

What quadrant is 1150° in?

a)

Quadrant I

b)

Quadrant II

c)

Quadrant III

d)

Quadrant IV

18.

Which angle is not coterminal to angle 45°?

a)

405°

b)

-315°

c)

765°

d)

-45°

19.

What is the reference angle of -275°?

a)

-85°

b)

85°

c)

5°

d)

-5°

20.

$-\frac{13\pi}{4}$

Which quadrant is the angle in?

a)

Quadrant I

b)

Quadrant II

c)

Quadrant III

d)

Quadrant IV

21.

Which angle is coterminal to $\frac{2\pi}{3}$

a)

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

b)

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

c)

$2\pi$

d)

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

22.

240° is equal to how many radians?

a)

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

b)

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

c)

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

d)

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

23.

$\frac{13\pi}{4}$

What quadrant is the angle located?

a)

Quadrant I

b)

Quadrant II

c)

Quadrant III

d)

Quadrant IV

24.

sin θ 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

25.

cos θ 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

26.

$\tan\theta$ 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

27.

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

a)

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

b)

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

c)

$\frac{1}{2}$

d)

$-\frac{1}{2}$

28.

Find cos 225⁰

a)

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

b)

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

c)

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

d)

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

29.

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

a)

$\sqrt{3}$

b)

$-\sqrt{3}$

c)

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

d)

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

30.

csc 330⁰

a)

2

b)

-2

c)

√2

d)

-√2

31.

Find $\sec\ \frac{\pi}{2}$

a)

undef

b)

0

c)

1

d)

-1

32.

Find $\cot\ \frac{\pi}{4}$

a)

-1

b)

$-\sqrt{3}$

c)

$\sqrt{3}$

d)

1

33.

What is a complete circle in radians?

a)

$\pi$

b)

$2\pi$

c)

$\frac{\pi}{2}$

d)

$1$

34.

What are the exact coordinates on the unit circle?

\frac{3\pi}{4}

a)

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

b)

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

c)

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

d)

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

35.

Identify the Positive angle in both radians and degrees that represent point H.

a)

$150\degree,\ \frac{5\pi}{6}$

b)

$135\degree,\ \frac{3\pi}{4}$

c)

$180\degree,\ \pi$

d)

$210\degree,\ \frac{7\pi}{6}$

36.

Identify the Positive angle in both radians and degrees that represent point D.

a)

$60\degree,\ \frac{\pi}{3}$

b)

$45\degree,\ \frac{\pi}{4}$

c)

$-60\degree,\ -\frac{\pi}{3}$

d)

$90\degree,\ \frac{\pi}{2}$

37.

Name the angle indicated by the graph in both radians and degrees.

a)

$-135\degree,\ -\frac{3\pi}{4}$

b)

$225\degree,\ \frac{5\pi}{4}$

c)

$-120\degree,\ -\frac{2\pi}{3}$

d)

$210\degree,\ \frac{7\pi}{6}$

38.

Name the angle indicated by the graph in both radians and degrees.

a)

$300\degree,\ \frac{5\pi}{3}$

b)

$315\degree,\ \frac{7\pi}{4}$

c)

$-60\degree,\ -\frac{\pi}{3}$

d)

$-300\degree,\ -\frac{5\pi}{3}$

39.

Find the exact value of the trig ratio.
$\cos\left(-120\degree\right)$

a)

$-\frac{1}{2}$

b)

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

c)

$\frac{1}{2}$

d)

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

40.

Find the exact value of the trig ratio.
$\sin\left(-\frac{11\pi}{6}\right)$

a)

$-\frac{1}{2}$

b)

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

c)

$\frac{1}{2}$

d)

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

41.

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

42.

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

43.

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

44.

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

45.

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

46.

60 miles per hour into meters per second

a)

28.6 meters per second

b)

28.6 meters per minute

c)

26.8 meters per second

d)

26.8 meters per minute

47.

1100 feet per second into miles per hour

a)

755 miles per hour

b)

760 miles per hour

c)

765 miles per hour

d)

750 miles per hour

48.

53 yards per hour into inches per week

a)

320,544 inches per week

b)

321,560 inches per week

c)

210,589 inches per week

d)

210,987 inches per week

49.

721 lbs per week into kilograms per second

a)

.54 kilograms per second

b)

.0054 kilograms per second

c)

.00054 kilograms per second

d)

.054 kilograms per second

6.6 -6.10 Review - Unit Circle, Circular Motion, Radians (PC)

Total questions: 49

Worksheet time: 52mins

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