Free Printable PreCalculus 11 (NS) Radicals and Trig Review

1.

$\sin\left(60^{\circ}\right)$

a)

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

b)

$\frac{1}{2}$

c)

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

d)

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

2.

$\sin\left(30^{\circ}\right)$

a)

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

b)

$\frac{1}{2}$

c)

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

d)

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

3.

$\sin\left(45^{\circ}\right)$

a)

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

b)

$\frac{1}{2}$

c)

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

d)

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

4.

$\cos\left(45^{\circ}\right)$

a)

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

b)

$\frac{1}{2}$

c)

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

d)

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

5.

$\cos\left(30^{\circ}\right)$

a)

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

b)

$\frac{1}{2}$

c)

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

d)

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

6.

$\cos\left(60^{\circ}\right)$

a)

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

b)

$\frac{1}{2}$

c)

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

d)

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

7.

$\tan\left(45^{\circ}\right)$

a)

$1$

b)

$\sqrt[]{3}$

c)

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

d)

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

8.

$\tan\left(30^{\circ}\right)$

a)

$1$

b)

$\sqrt[]{3}$

c)

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

d)

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

9.

$\tan\left(60^{\circ}\right)$

a)

$1$

b)

$\sqrt[]{3}$

c)

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

d)

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

10.

sin(120^o)

a)

- ½

b)

√3/2

c)

2√3 /3

d)

½

11.

tan(3π/4)

a)

√2/2

b)

-√2/2

c)

√3/2

d)

-1

12.

cos(2π)

a)

0

b)

1

c)

UND

d)

-1

13.

tan(3π/2)

a)

-1

b)

UND

c)

√2

d)

-√3/3

14.

sin(315^o)

a)

√2/2

b)

-√3/2

c)

½

d)

-√2/2

15.

tan(11π/6)

a)

- √3/2

b)

-1

c)

-√3

d)

-√3/3

16.

What quadrant does 45° belong to?

a)

Quadrant 1

b)

Quadrant 2

c)

Quadrant 3

d)

Quadrant 4

17.

What quadrant does 198° belong to?

a)

Quadrant 1

b)

Quadrant 2

c)

Quadrant 3

d)

Quadrant 4

18.

What quadrant does 153° belong to?

a)

Quadrant 1

b)

Quadrant 2

c)

Quadrant 3

d)

Quadrant 4

19.

What quadrant does 345° belong to?

a)

Quadrant 1

b)

Quadrant 2

c)

Quadrant 3

d)

Quadrant 4

20.

sin 45° would be:

a)

Positive

b)

Negative

21.

cos 192° would be:

a)

Positive

b)

Negative

22.

tan 192° would be:

a)

Positive

b)

Negative

23.

csc 320° would be:

a)

Positive

b)

Negative

24.

In which quadrant must θ lie in for the following to be true?

sin θ < 0 & cos θ > 0

a)

Quadrant 1

b)

Quadrant 2

c)

Quadrant 3

d)

Quadrant 4

25.

In which quadrant must θ lie in for the following to be true?

sin θ > 0 & tan θ > 0

a)

Quadrant 1

b)

Quadrant 2

c)

Quadrant 3

d)

Quadrant 4

26.

In which quadrant must θ lie in for the following to be true?

sin θ > 0 & cot θ < 0

a)

Quadrant 1

b)

Quadrant 2

c)

Quadrant 3

d)

Quadrant 4

27.

Which equation describes the algebraic relationship between sine, cosine, and tangent?

a)

$\sin x-\cos x=\tan x$

b)

$\cos x\div\sin x=\tan x$

c)

$\sin^2x+\cos^2x=\tan^2x$

d)

$\sin x\div\cos x=\tan x$

28.

In which quadrant would you find an angle measuring -740°

a)

1

b)

2

c)

3

d)

4

29.

What is the reference angle for 125°?

a)

235°

b)

125°

c)

75°

d)

55°

30.

Which is a coterminal angle to the angle shown?

a)

613 $\degree$

b)

73 $\degree$

c)

-117 $\degree$

d)

17 $\degree$

31.

What is the reference angle for -30°?

a)

150°

b)

30°

c)

80°

d)

60°

32.

What is the reference angle?

a)

163 $\degree$

b)

73 $\degree$

c)

27 $\degree$

d)

107 $\degree$

33.

Which of the following is closest to the measure of the angle shown?

a)

30º

b)

40º

c)

395º

d)

440º

34.

Which quadrant does the following angle terminate in?

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

a)

I

b)

II

c)

III

d)

IV

35.

Which quadrant does the following angle terminate in?

$-655\degree$

a)

I

b)

II

c)

III

d)

IV

36.

Which quadrant does the following angle terminate in?

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

a)

I

b)

II

c)

III

d)

IV

37.

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.

38.

Negative angles are measured in which direction from standard position?

a)

Clockwise

b)

Counterclockwise

39.

Positive angles are measured in which direction from standard position?

a)

Clockwise

b)

Counterclockwise

40.

In which quadrant is -570⁰

a)

I

b)

II

c)

III

d)

IV

41.

In which quadrant would you find an angle measuring -700°?

a)

1

b)

2

c)

3

d)

4

42.

-500^o is in which quadrant?

a)

I

b)

II

c)

III

d)

IV

43.

570° is found in which quadrant?

a)

Quadrant 1

b)

Quadrant 2

c)

Quadrant 3

d)

Quadrant 4

44.

Find a coterminal angle to 45°.

a)

360°

b)

405°

c)

315°

d)

295°

45.

Find a coterminal angle to 5°.

a)

365°

b)

255°

c)

-220°

d)

-365°

46.

In what quadrant is -285°?

a)

I

b)

II

c)

III

d)

IV

47.

Find a coterminal angle to -90°.

a)

-450°

b)

90°

c)

180°

d)

-180°

48.

Find a coterminal angle to -27°.

a)

-387°

b)

27°

c)

323°

d)

-393°

49.

Find an angle coterminal with an angle which measures 11π ∕ 3.

a)

17 π / 3

b)

4π ∕ 3

c)

π ∕ 3

d)

8π ∕ 3

50.

Find an angle coterminal with an angle measuring 17π / 4 radians.

a)

π ∕ 3

b)

5π ∕ 4

c)

π ∕ 4

d)

13π ∕ 4

51.

What is positive in Q4?

a)

all trig functions

b)

sine

c)

cosine

d)

tangent

52.

If θ is an angle in Quadrant II, which trig ratios will be positive

a)

sin θ

b)

cos θ

c)

tan θ

d)

cos θ and sin θ

53.

Are the given angles coterminal?
35° and -325°

a)

Yes, they are coterminal

b)

No, they are not coterminal

54.

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

55.

For what angles are sine and cosine the same?

a)

0^o

b)

45^oand 135⁰

c)

45^oand 225⁰

d)

45^oand 315⁰

56.

Find the measure of each angle

a)

A

b)

B

c)

C

d)

D

57.

Find the measure of each angle

a)

A

b)

B

c)

C

d)

D

58.

Find the measure of each angle

a)

A

b)

B

c)

C

d)

D

59.

How many radians are there in half a circle?

a)

2 $\pi$

b)

180^o

c)

360^o

d)

$\pi$

60.

Convert 150⁰ to radians

a)

5π/6

b)

3π/4

c)

7π/6

d)

2π/3

61.

What is 4π/3 radians in degrees?

a)

120

b)

240

c)

210

d)

270

62.

What is a radian?

a)

a central angle created when the radius equals the arc length

b)

a central angle created when the radius is twice as big as the arc length

c)

a central angle created when the radius is half as big as the arc length

d)

A central angle created when one radius equals the other radius

63.

The distance along an arc measured in linear units.

a)

area of a sector

b)

arc length

c)

arc of a circle

d)

sector of a circle

64.

In circle O, the radius is 4, and the measure of minor arc AB is 120 degrees. Find the length of minor arc AB to the nearest integer.

a)

5

b)

9

c)

8

d)

6

65.

In circle O, the radius is 4, and the length of minor arc AB is 4.2 feet. Find the measure of minor arc AB to the nearest degree.

a)

90

b)

60

c)

55

d)

113

66.

Find the length of the bold arc.

a)

61.3ft

b)

20.4ft

c)

7351.3ft

d)

22,068ft

67.

Solve\ \ \ 4\cos x+3=5\ \ \ for\ 0\le x<360\degree

a)

$x\ =\ 60\degree,\ 120\degree$

b)

$x\ =\ 60\degree,\ 300\degree$

c)

$x\ =\ 30\degree,\ 150\degree$

d)

$x\ =\ 30\degree,\ 330\degree$

68.

$Solve\ \ \tan\ x\ +\ \sqrt{3}\ =\ 0\ \ for\ 0\ \le\ x\ <\ 360\degree$

a)

$30\degree,\ 210\degree$

b)

$150\degree,\ 330\degree$

c)

$60\degree,\ 240\degree$

d)

$120\degree,\ 300\degree$

69.

$Solve\ \ 3\tan x\ +\ 2\ =\ 2\ \ for\ \ 0\ \le\ x\ <\ 2\pi$

a)

No solution

b)

$0,\ \pi$

c)

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

d)

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

70.

$Solve\ \ 3\sin x\ +\ 4\ =\ 6\ \ for\ \ 0\ \le\ x\ <\ 360\degree.$ Round to the nearest 10th of a degree.

a)

$41.8\degree,\ 138.2\degree$

b)

$48.1\degree,\ 131.9\degree$

c)

$221.8\degree,\ 318.2\degree$

d)

$228.1\degree,\ 311.9\degree$

71.

Solve the equation for

0\le x<2\pi

. Round all answers to the nearest hundredth (2 decimals). Pick TWO solutions for the problem:

\sin x=0.345

a)

0.35

b)

3.49

c)

2.79

d)

5.93

72.

Solve the equation for

0\le x<2\pi

. Round all answers to the nearest hundredth (2 decimals). Pick TWO solutions for the problem:

\tan x=10

a)

1.47

b)

4.61

c)

1.67

d)

4.81

73.

Solve the equation for

0\le x<2\pi

. Round all answers to the nearest hundredth (2 decimals). Pick TWO solutions for the problem:

\cos x=-\frac{2}{3}

a)

2.30

b)

3.98

c)

0.84

d)

5.44

74.

Solve the equation for

0\le x<2\pi

. Round all answers to the nearest hundredth (2 decimals). Pick TWO solutions for the problem:

\cos x=0.7

a)

0.80

b)

5.49

c)

1.48

d)

4.80

75.

Solve the equation for

0\le x<2\pi

. Round all answers to the nearest hundredth (2 decimals). Pick TWO solutions for the problem:

\sin x=-0.95

a)

4.39

b)

5.03

c)

2.74

d)

-1.25

76.

Solve the equation for

0\le x<2\pi

. Round all answers to the nearest hundredth (2 decimals). Pick TWO solutions for the problem:

\cos x=-\frac{6}{7}

a)

0.54

b)

5.74

c)

2.60

d)

3.68

77.

Solve the equation for

0\le x<2\pi

. Round all answers to the nearest hundredth (2 decimals). Pick TWO solutions for the problem:

\tan x=-\frac{3}{4}

a)

-0.64

b)

2.50

c)

5.64

d)

3.79

78.

Solve for x:
$2\tan\left(x\right)=0$

a)

0

b)

π

c)

$\frac{\pi}{3}$

d)

$\frac{π}{4}$

79.

Draw an angle that measures 330° in standard position.

a)

b)

c)

d)

80.

Draw an angle that measures $-250\degree$ in standard postion.

a)

b)

c)

d)

81.

The exact value of $\left(\frac{\sin\pi}{3}\right)\left(\frac{\cos2\pi}{3}\right)$ is

a)

$\frac{1}{2}$

b)

$-\frac{1}{2}$

c)

$\frac{-\sqrt[]{3}}{4}$

d)

$\frac{\sqrt[]{3}}{4}$

82.

The exact value of $\sin\ \frac{7\pi}{12}$ is

a)

0.03

b)

$\frac{\sqrt[]{3}-1}{2\sqrt[]{2}}$

c)

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

d)

$\frac{\sqrt[]{3}+1}{2\sqrt[]{2}}$

83.

Use the Unit Circle to determine the exact value of:

\tan45\degree-\sin60\degree

a)

$\frac{2\sqrt{3}-3\sqrt{2}}{6}$

b)

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

c)

$\frac{-\sqrt{3}}{6}$

d)

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

84.

Use the Unit Circle to determine the exact value of:

1-\sin^230\degree-\sin^260\degree

a)

$\frac{1}{4}$

b)

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

c)

$0$

d)

$1$

85.

Use the Unit Circle to determine the exact value of:

\frac{2\cos30\degree}{\cos\left(-120\degree\right)}

a)

$-2\sqrt{3}$

b)

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

c)

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

d)

$\sqrt{3}$

86.

Use the Unit Circle to determine the exact value of:

\frac{\sin\left(\frac{-2\pi}{3}\right)}{\sin\left(\frac{\pi}{3}\right)+\cos\left(\frac{5\pi}{4}\right)}

a)

$-3-\sqrt{6}$

b)

$\frac{-3+\sqrt{6}}{5}$

c)

$-1-\sqrt{6}$

d)

$\frac{\sqrt{2}+\sqrt{6}}{5}$

87.

Use the Unit Circle to determine the exact value of:

$\cos\pi+\sin\ \frac{3\pi}{2}$

a)

2

b)

-2

c)

1

d)

-1

88.

Evaluate the following expression: $\sin\ \frac{2\pi}{3}\cos\pi-\cos\ \frac{\pi}{4}\sin\ \frac{\pi}{6}$

a)

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

b)

$\frac{-\sqrt[]{3}-\sqrt[]{2}}{4}$

c)

$\frac{-2\sqrt[]{3}-\sqrt[]{2}}{4}$

d)

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

89.

Evaluate the expression: $\sin\ \frac{7\pi}{6}\sin\ \frac{5\pi}{3}$

a)

$\frac{-\sqrt[]{3}}{4}$

b)

$\frac{\sqrt[]{3}}{4}$

c)

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

d)

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

90.

Evaluate the expression: $\sin\ \pi\ \cos\ \frac{3\pi}{4}+\cos\pi\ \cos\ \frac{11\pi}{6}$

a)

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

b)

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

c)

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

d)

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

91.

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

a)

$y$

b)

$x$

c)

\frac{x}{y}

d)

$\frac{y}{x}$

92.

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

a)

y

b)

$x$

c)

$\frac{x}{y}$

d)

$\frac{y}{x}$

93.

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

a)

\frac{y}{r}

b)

$\frac{x}{r}$

c)

$\frac{r}{y}$

d)

$\frac{y}{x}$

PreCalculus 11 (NS) Radicals and Trig Review

Total questions: 93

Worksheet time: 3hrs 41mins

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