Free Printable Circles Review (special rights, radians, unit circle, arc length

1.

How many radians does a circle have?

a)

360 degrees

b)

2pi radians

c)

pi radians

d)

^{2 radians}

2.

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

3.

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

4.

Convert π radians to degrees.

a)

90⁰

b)

180⁰

c)

360⁰

d)

60⁰

5.

How many radians are there in half a circle?

a)

2 pi

b)

180^o

c)

360^o

d)

pi

6.

The length of an arc is 18cm and the radius of the circle is 6cm. What is the radian measure of the central angle?

a)

3 radian

b)

2 radian

c)

4 radian

d)

2π radian

7.

Find the arc length.

a)

3π/4 ft

b)

39π/4 ft

c)

13π/4 ft

d)

4π/13 ft

8.

Find the arc length

a)

7 cm

b)

28π cm

c)

7π cm

d)

28 cm

9.

The length of an arc is 18cm and the radius of the circle is 6cm. What is the radian measure of the central angle?

a)

3 radian

b)

2 radian

c)

4 radian

d)

2π radian

10.

A central angle measure 4.5 radians and has an arc of 35 inches. What is the radius of the circle?

a)

7.78 inches

b)

8.21 inches

c)

157.5 inches

d)

7 inches

11.

$\frac{2\pi}{3}$ lies in which quadrant?

a)

QI

b)

QII

c)

QIII

d)

QIV

12.

Convert 100⁰ to radians

a)

5π/9

b)

π/2

c)

5π/8

d)

5π/6

13.

Convert the following to radians:
720⁰

a)

3π

b)

4π

c)

5π

14.

Select the correct sketch of the angle in standard position: $285\degree$

a)

b)

c)

d)

15.

To convert from degrees to RADIANS

a)

multiply by

\frac{π}{180°}

b)

multiply by
$\frac{180°}{π}$

c)

multiply by
$\frac{π}{\sqrt{2}}$

d)

multiply by
$\frac{π}{\sqrt{3}}$

16.

To convert from radians to DEGREES

a)

multiply by

\frac{π}{180°}

b)

multiply by
$\frac{180°}{π}$

c)

multiply by
$\frac{π}{\sqrt{2}}$

d)

multiply by
$\frac{π}{\sqrt{3}}$

17.

In this 45-45-90 triangle, I have been given a leg, so to find the other leg I...

a)

Multiply that leg by 2

b)

Use the same length for the second leg

c)

Multiply that leg by √2

d)

Divide that leg by √2

18.

What is the length of y in this picture?

a)

45

b)

5√2

c)

90

d)

5

19.

In this 45-45-90 triangle, I have been given the length of a leg. How do I find the length of the hypotenuse?

a)

It is the same length as the given leg.

b)

Multiply that leg's length by √2.

c)

Multiply that leg's length by 2.

d)

Divide that leg's length by √2.

20.

What is the length of x in this 45-45-90 triangle?

a)

4√2

b)

4

c)

8

d)

4√3

21.

I have been given a hypotenuse in this 45-45-90 triangle. How do I find the length of a leg of the triangle?

a)

Multiply by √2

b)

Divide by √2

c)

It's the same length as the hypotenuse.

d)

Divide by 2

22.

What is the length of y in this 45-45-90 triangle?

a)

8√2

b)

4√2

c)

4

d)

8

23.

I have been given the short leg in this 30-60-90 triangle. How do I find the long leg?

a)

Multiply 4 by 2

b)

Multiply 4 by √3

c)

Multiply 4 by √2

d)

Divide 4 by 2

24.

I have been given the short leg in this 30-60-90 triangle. How do I find the length of the hypotenuse?

a)

Multiply 4 by 2

b)

Multiply 4 by √3

c)

Multiply 4 by √2

d)

Divide 4 by √3

25.

Find the value of y.

a)

8

b)

4

c)

2√3

d)

8√3

26.

Determine the value of x.

a)

x = 10√2

b)

x = 10

c)

x = 5√3

d)

x = 5√6

27.

Choose the correct values for x and y in the right triangle.

a)

$x=3$

b)

$x=3\sqrt{2}$

c)

$y\ =\ 6$

d)

$y=6\sqrt{2}$

28.

Choose the correct values for x and y in the right triangle.

a)

$x=\frac{5\sqrt{6}}{2}$

b)

$x=5$

c)

$y\ =\ 10$

d)

$y=10\sqrt{3}$

29.

Choose the correct values for x and y in the right triangle.

a)

$x=\frac{11\sqrt{3}}{3}$

b)

$x=11$

c)

$y\ =\ 22$

d)

$y=11\sqrt{3}$

30.

a)

a=√6 b=√2

b)

a=4 b=2

c)

a=√6 b=2

d)

a=2 b4

31.

sin 7π/6

a)

1/2

b)

-1/2

c)

√3/2

d)

-√3/2

32.

cos (π/4)

a)

√3/2

b)

√2/2

c)

1/2

d)

1

33.

cos(5π/3)

a)

-√2/2

b)

-1/2

c)

1/2

d)

√3/2

34.

Using θ as a reference angle, mark the triangle sides as Opp, Adj, and Hyp.

Label these on the triangle on your paper.

a)

x

1.

Adj

b)

y

2.

Opp

c)

OP

3.

Hyp

35.

Look at YOUR unit circle. What is the reference angle for $\frac{4\pi}{3}$ ?

Reference angle = (a)

Choose from the below words

$\frac{\pi}{3}$

$\frac{\pi}{4}$

$\frac{\pi}{6}$

$\frac{\pi}{2}$

36.

Look at YOUR unit circle. What is the reference angle for $\frac{7\pi}{4}$ ?

Reference angle = (a)

Choose from the below words

$\frac{\pi}{4}$

$\frac{\pi}{6}$

$\frac{\pi}{2}$

$\frac{\pi}{3}$

37.

Unlike right triangle trigonometry, sine and cosine may be negative.

Thinking about how sine, cosine, and tangent relate to (x,y) coordinate pairs on the unit circle, find the quadrants where:

sine is positive: (a) & (b)

sine is negative: (c) & (d)

Choose from the below words

I

II

III

IV

38.

Unlike right triangle trigonometry, sine and cosine may be negative.

Thinking about how sine, cosine, and tangent relate to (x,y) coordinate pairs on the unit circle, find the quadrants where:

cosine is positive: (a) & (b)

cosine is negative: (c) & (d)

Choose from the below words

I

IV

II

III

39.

Find the exact value of the following trig expressions.

Try to remember these results without looking at the unit circle.

$\sin\left(\frac{\pi}{3}\right)=$ (a)

$\sin\left(\frac{7\pi}{6}\right)=$ (b)

$\cos\left(\frac{5\pi}{4}\right)=$ (c)

$\cos\left(-\frac{\pi}{3}\right)=$ (d)

Choose from the below words

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

$-\frac{1}{2}$

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

$\frac{1}{2}$

0

1

-1

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

$\frac{\sqrt[]{2}}{2}$

40.

a)

b)

c)

d)

41.

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)

42.

Evaluate cos(225°)

a)

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

b)

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

c)

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

d)

$-\frac{1}{2}$

43.

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)

44.

Drag and drop the degree measures of the unit circle into the correct space.

a)

270

b)

280

c)

225

d)

215

e)

145

f)

150

g)

0

h)

330

i)

45

j)

120

1

2

3

4

5

6

7

1)

2)

3)

4)

5)

6)

7)

45.

Drag and drop the (x,y)-coordinates of the unit circle into the correct space.

a)

$\frac{\sqrt{3}}{2},\frac{1}{2}$

b)

$-\frac{\sqrt{3}}{2},-\frac{1}{2}$

c)

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

d)

$-\frac{1}{2},-\frac{\sqrt{\ 3}}{2}$

e)

$1,0$

f)

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

g)

$-1,0$

h)

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

i)

$\frac{1}{2},\ \frac{\sqrt{3}}{2}$

j)

$0,1$

1

2

3

4

5

6

7

1)

2)

3)

4)

5)

6)

7)

46.

Drag and drop the radian measures of the unit circle into the correct space.

a)

$\frac{11\pi}{4}$

b)

$\frac{7\pi}{4}$

c)

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

d)

$\frac{5\pi}{4}$

e)

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

f)

$\frac{\pi}{3}$

g)

$\frac{\pi}{6}$

h)

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

i)

$\pi$

j)

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

1

2

3

4

5

6

7

1)

2)

3)

4)

5)

6)

7)

47.

Convert the following degree measures to radians:

a)

75

1.

$\frac{5\pi}{12}$ radians

b)

180

2.

$\pi$ radians

c)

600

3.

$\frac{10\pi}{3}$ radians

d)

-210

4.

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

e)

-450

5.

$-\frac{5\pi}{2}$ radians

48.

Convert the following radian measures to degrees:

a)

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

1.

-45 degrees

b)

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

2.

-20 degrees

c)

$\frac{26\pi}{9}$

3.

520 degrees

d)

$\frac{5\pi}{4}$

4.

225 degrees

e)

$\frac{25\pi}{6}$

5.

750 degrees

49.

What is the exact value of $\sin\left(\frac{7\pi}{6}\right)$ ?

a)

$\frac{1}{2}$

b)

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

c)

$-\frac{1}{2}$

d)

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

50.

$\sin\ 30\degree=$

a)

$\frac{1}{2}$

b)

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

c)

0

d)

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

Circles Review (special rights, radians, unit circle, arc length

Total questions: 50

Worksheet time: 59mins

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