Free Printable Intro to Trig Review (Angles, Arcs, Trig Functions at Point)

1.

What is $225\degree$ in radians?

a)

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

b)

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

c)

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

d)

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

2.

What is $\frac{11\pi}{6}$ radians in degrees?

a)

30

b)

330

c)

360

d)

300

3.

What is $\frac{2\pi}{3}$ radians in degrees?

a)

$150\degree$

b)

$120\degree$

c)

$180\degree$

d)

$30\degree$

4.

What is $270\degree$ in radians?

a)

$\frac{\pi}{4}$

b)

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

c)

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

d)

$\frac{\pi}{2}$

5.

What is $\frac{7\pi}{4}$ in degrees?

a)

$300\degree$

b)

$135\degree$

c)

$315\degree$

d)

$45\degree$

6.

Convert π radians to degrees.

a)

90⁰

b)

180⁰

c)

360⁰

d)

60⁰

7.

Convert 150⁰ to radians

a)

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

b)

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

c)

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

d)

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

8.

Convert $\frac{\pi}{3}$ radians to degrees

a)

60⁰

b)

30⁰

c)

90⁰

d)

45⁰

9.

Convert $\frac{\pi}{4}$ to degrees

a)

90⁰

b)

45⁰

c)

60⁰

d)

30⁰

10.

$\frac{8\pi}{3}$ is equivalent to what degree measure?

a)

$480\degree$

b)

$240\degree$

c)

$800\degree$

d)

$24\degree$

11.

Convert 510^o to Radians

a)

25π / 3

b)

23π / 8

c)

17π / 6

d)

51π / 8

12.

How many DEGREES are in a circle?

a)

180^o

b)

360^o

c)

π rad

d)

2π rad

13.

How many RADIANS are in a circle?

a)

180^o

b)

360^o

c)

π rad

d)

2π rad

14.

What is 10° in radians?

a)

π/18

b)

2π/5

c)

π/6

d)

π/9

15.

what is 165° in radians?

a)

13π/12

b)

7π/12

c)

19π/12

d)

11π/12

16.

What is 285° in radians?

a)

15π/12

b)

13π/12

c)

19π/12

d)

7π/3

17.

Convert -40^o into Radians

a)

-4π / 8

b)

-8π / 9

c)

-2π / 9

d)

-5π / 8

18.

what is π/12 in degrees?

a)

75°

b)

15°

c)

105°

d)

60°

19.

Find the arc length indicated by the bolded arc.

a)

8.3 in

b)

7.2 in

c)

6.8 in

d)

6.4 in

20.

Find the arc length indicated by the bolded arc.

a)

17.3 km

b)

79.1 km

c)

95.0 km

d)

99.0 km

21.

Find the arc length indicated by the bolded arc.

a)

8.4 mi

b)

9.4 mi

c)

60.2 mi

d)

117.8 mi

22.

Find the length of the bold arc. Leave $\pi$ in your answer.

a)

5688π ft

b)

15.8π ft

c)

150.4π ft

d)

54,150 ft

23.

The formula for the arc length given an angle measurement in radians is

a)

$2\pi r\theta$

b)

$r^2$

c)

$r\theta$

24.

Find the area of the shaded sector of circle O. The radius is 6 inches and the central angle is 100°. Express answer to the nearest tenth of a square inch.

a)

9.2 sq. in.

b)

10.5 sq. in.

c)

31.4 sq. in.

d)

38.2 sq. in.

25.

Find the area of each sector.

a)

52.4 in²

b)

18,864 in²

c)

60 in2

d)

10.47 in

26.

Find the area of each sector.

a)

4248 m²

b)

7.9 m²

c)

2827.4 m²

d)

11.8 m²

27.

Find the area of each sector.

a)

4248 m²

b)

7.9 m²

c)

2827.4 m²

d)

11.8 m²

28.

Name the quadrant the point is in:

\left(-13,\ 2\right)

a)

1

b)

2

c)

I

d)

II

e)

IV

29.

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)

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

30.

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)

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

31.

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)

$\frac{5}{6}$

32.

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)

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

33.

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)

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

34.

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)

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

35.

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)

$-\frac{10}{9}$

36.

Given the point (-4, -3) on the terminal side of the angle $\theta.$

What is sin $\theta?$

a)

3/5

b)

-5/4

c)

-3/5

d)

-4/5

37.

sin $\theta$ =

a)

$\frac{y}{r}$

b)

$\frac{x}{r}$

c)

$\frac{y}{x}$

d)

$\frac{r}{x}$

38.

cos $\theta$ =

a)

$\frac{y}{r}$

b)

$\frac{x}{r}$

c)

$\frac{y}{x}$

d)

$\frac{r}{x}$

39.

csc $\theta$ =

a)

$\frac{r}{y}$

b)

$\frac{r}{x}$

c)

$\frac{y}{x}$

d)

$\frac{x}{y}$

40.

sec $\theta$ =

a)

$\frac{r}{y}$

b)

$\frac{r}{x}$

c)

$\frac{y}{x}$

d)

$\frac{x}{y}$

41.

cot $\theta$ =

a)

$\frac{r}{y}$

b)

$\frac{r}{x}$

c)

$\frac{y}{x}$

d)

$\frac{x}{y}$

42.

$\frac{r}{x}$ =

a)

cos $\theta$

b)

$\sec\ \theta$

c)

$\sin\ \theta$

d)

$\csc\ \theta$

43.

$\frac{x}{r}$ =

a)

cos $\theta$

b)

$\sec\ \theta$

c)

$\sin\ \theta$

d)

$\csc\ \theta$

44.

$\frac{y}{r}$ =

a)

cos $\theta$

b)

$\sec\ \theta$

c)

$\sin\ \theta$

d)

$\csc\ \theta$

45.

tan $\theta$ =

a)

$\frac{r}{y}$

b)

$\frac{r}{x}$

c)

$\frac{y}{x}$

d)

$\frac{x}{y}$

46.

What quadrant is "x" in?

a)

Q1

b)

Q2

c)

Q3

d)

Q4

47.

What are the negative and positive coterminal angles of 120°?

a)

420°, -240°

b)

480°, -240°

c)

300°, -360°

d)

0°, -250°

48.

What are the negative and positive coterminal angles of -165°?

a)

435°, -545°

b)

185°, -305°

c)

195°, -525°

d)

125°, -185°

49.

Which angle is COTERMINAL to $\frac{\pi}{4}$ ?

a)

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

b)

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

c)

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

d)

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

50.

What is an example of a pair of complementary angles?

a)

13° and 45°

b)

10° and 170°

c)

81° and 9°

d)

90° and 3°

51.

What are complementary angles?

a)

Angles that add up to 180°

b)

Angles that add up to 90°

c)

Angles that are equal to each other

d)

Angles that are opposite of each other when lines intersect.

52.

What are supplementary angles?

a)

Angles that add up to 180°

b)

Angles that add up to 90°

c)

Angles that are equal to each other

d)

Angles that are opposite of each other when lines intersect

53.

If you split a circle into 6 equal parts, how many degrees will each section be?

a)

30/pi^o

b)

60^o

c)

30^o

d)

60/pi^o

54.

How do you convert from degrees to radians?

a)

multiply by the factor
π/180

b)

multiply by the factor 180/
π

c)

use your calculator

d)

ask siri

55.

What are co-terminal angles?

a)

angles that share the same terminal side

b)

angles that are supplementary

c)

angles that are complimentary

d)

angles that are opposite each other

56.

What is the compliment of an angle?

a)

You look lovely today

b)

Angle + compliment= 180 degrees

c)

Angle + compliment = 90 degrees

d)

A radian

57.

Name the reciprocal trig functions.

a)

sin, cos, tan

b)

sin⁻¹, cos⁻¹, tan⁻¹

c)

csc, cot, sec

d)

dasher, dancer, prancer

58.

Identify the marsupial

a)

b)

c)

59.

What is a marsupial?

a)

an animal that eats leaves

b)

an animal with a pouch to carry its babies

c)

an animal that loves to run

d)

an animal that has a pouch to carry its food

60.

Why was Alcatraz chosen as a prison for the worst offenders?

a)

It was thought to be hard to escape since it was an island.

b)

It was very far from civilization.

c)

It was in an area where it was possible to hire cheap labor as prison guards.

d)

It was a well built facility.

61.

Susan B. Anthony was famous for what?

a)

Becoming President

b)

Making Sandwiches

c)

Women's Suffrage Movement

d)

Being a Nurse in the Civil War

62.

What does suffrage mean?

a)

being in pain

b)

getting rid of slavery

c)

the right to vote

d)

the right to equal pay

63.

What team logo is this?

a)

Seattle Mariners

b)

South Carolina Tarheels

c)

Southpaw Panthers

d)

Seattle Space Needles

64.

What team logo is this?

a)

Oakland Raiders

b)

Oakland Athletics

c)

Arkansas Avengers

d)

Alaska A's

65.

A literary work is a satire when it ________

a)

Finds fault

b)

Humorously criticizes to improve a situation

c)

Proves laughter

d)

Teaches a lesson for social improvement

Intro to Trig Review (Angles, Arcs, Trig Functions at Point)

Total questions: 65

Worksheet time: 2hrs 10mins

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