Quiz about PreCalculus 11 (NS) Radicals and Trig Review

Question 1

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 2

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 3

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 4

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 5

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 6

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 7

$$ an\left(45^{\circ} ight)$$

Accepted Answer

$$1$$

Answer

$$\sqrt[]{3}$$

Answer

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

Answer

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

Question 8

$$ an\left(30^{\circ} ight)$$

Accepted Answer

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

Answer

$$1$$

Answer

$$\sqrt[]{3}$$

Answer

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

Question 9

$$ an\left(60^{\circ} ight)$$

Accepted Answer

$$\sqrt[]{3}$$

Answer

$$1$$

Answer

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

Answer

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

Question 10

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

Accepted Answer

$$\sin x\div\cos x= an x$$

Answer

$$\sin x-\cos x= an x$$

Answer

$$\cos x\div\sin x= an x$$

Answer

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

Question 11

Which is a coterminal angle to the angle shown?

Accepted Answer

613 $$\degree$$

Answer

73 $$\degree$$

Answer

-117 $$\degree$$

Answer

17 $$\degree$$

Question 12

What is the reference angle?

Accepted Answer

73 $$\degree$$

Answer

163 $$\degree$$

Answer

27 $$\degree$$

Answer

107 $$\degree$$

Question 13

Which quadrant does the following angle terminate in?

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

Accepted Answer

III

Answer

I

Answer

II

Answer

IV

Question 14

Which quadrant does the following angle terminate in?

$$-655\degree$$

Accepted Answer

I

Answer

II

Answer

III

Answer

IV

Question 15

Which quadrant does the following angle terminate in?

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

Accepted Answer

III

Answer

I

Answer

II

Answer

IV

Question 16

Standard position is when .....

Accepted Answer

the initial side of the angle is on the positive x-axis.

Answer

the initial side of the angle is on the negative x-axis.

Answer

the initial side of the angle is on the positive y-axis.

Answer

the initial side of the angle is on the negative y-axis.

Question 17

Negative angles are measured in which direction from standard position?

Accepted Answer

Clockwise

Answer

Counterclockwise

Question 18

Positive angles are measured in which direction from standard position?

Accepted Answer

Counterclockwise

Answer

Clockwise

Question 19

-500^o is in which quadrant?

Accepted Answer

III

Answer

I

Answer

II

Answer

IV

Question 20

What is positive in Q4?

Accepted Answer

cosine

Answer

all trig functions

Answer

sine

Answer

tangent

Question 21

The unit circle...

Accepted Answer

Has a radius of 1

Answer

Has center at (1,1)

Answer

Has a circumference of 1

Answer

Has a diameter of 1

Question 22

For what angles are sine and cosine the same?

Accepted Answer

45^oand 225⁰

Answer

0o

Answer

45^oand 135⁰

Answer

45^oand 315⁰

Question 23

Find the measure of each angle

Accepted Answer

B

Answer

A

Answer

C

Answer

D

Question 24

Find the measure of each angle

Accepted Answer

B

Answer

A

Answer

C

Answer

D

Question 25

Find the measure of each angle

Accepted Answer

D

Answer

A

Answer

B

Answer

C

Question 26

How many radians are there in half a circle?

Accepted Answer

$$\pi$$

Answer

2 $$\pi$$

Answer

180o

Answer

360o

Question 27

What is a radian?

Accepted Answer

a central angle created when the radius equals the arc length

Answer

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

Answer

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

Answer

A central angle created when one radius equals the other radius

Question 28

The distance along an arc measured in linear units.

Accepted Answer

arc length

Answer

area of a sector

Answer

arc of a circle

Answer

sector of a circle

Question 29

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.

Accepted Answer

8

Answer

5

Answer

9

Answer

6

Question 30

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.

Accepted Answer

60

Answer

90

Answer

55

Answer

113

Question 31

Find the length of the bold arc.

Accepted Answer

61.3ft

Answer

20.4ft

Answer

7351.3ft

Answer

22,068ft

Question 32

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 33

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

Accepted Answer

$$120\degree,\ 300\degree$$

Answer

$$30\degree,\ 210\degree$$

Answer

$$150\degree,\ 330\degree$$

Answer

$$60\degree,\ 240\degree$$

Question 34

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

Accepted Answer

$$0,\ \pi$$

Answer

No solution

Answer

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

Answer

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

Question 35

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

Accepted Answer

$$41.8\degree,\ 138.2\degree$$

Answer

$$48.1\degree,\ 131.9\degree$$

Answer

$$221.8\degree,\ 318.2\degree$$

Answer

$$228.1\degree,\ 311.9\degree$$

Question 36

Solve the equation for

$$0\le x<2\pi$$ . Round all answers to the nearest hundredth (2 decimals). Pick TWO solutions for the problem:
$$\sin x=0.345$$

Accepted Answer

0.35

Accepted Answer

2.79

Answer

3.49

Answer

5.93

Question 37

Solve the equation for

$$0\le x<2\pi$$ . Round all answers to the nearest hundredth (2 decimals). Pick TWO solutions for the problem:
$$ an x=10$$

Accepted Answer

1.47

Accepted Answer

4.61

Answer

1.67

Answer

4.81

Question 38

Solve the equation for

$$0\le x<2\pi$$ . Round all answers to the nearest hundredth (2 decimals). Pick TWO solutions for the problem:
$$\cos x=-\frac{2}{3}$$

Accepted Answer

2.30

Accepted Answer

3.98

Answer

0.84

Answer

5.44

Question 39

Solve the equation for

$$0\le x<2\pi$$ . Round all answers to the nearest hundredth (2 decimals). Pick TWO solutions for the problem:
$$\cos x=0.7$$

Accepted Answer

0.80

Accepted Answer

5.49

Answer

1.48

Answer

4.80

Question 40

Solve the equation for

$$0\le x<2\pi$$ . Round all answers to the nearest hundredth (2 decimals). Pick TWO solutions for the problem:
$$\sin x=-0.95$$

Accepted Answer

4.39

Accepted Answer

5.03

Answer

2.74

Answer

-1.25

Question 41

Solve the equation for

$$0\le x<2\pi$$ . Round all answers to the nearest hundredth (2 decimals). Pick TWO solutions for the problem:
$$\cos x=-\frac{6}{7}$$

Accepted Answer

2.60

Accepted Answer

3.68

Answer

0.54

Answer

5.74

Question 42

Solve the equation for

$$0\le x<2\pi$$ . Round all answers to the nearest hundredth (2 decimals). Pick TWO solutions for the problem:
$$ an x=-\frac{3}{4}$$

Accepted Answer

2.50

Accepted Answer

5.64

Answer

-0.64

Answer

3.79

Question 43

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

Accepted Answer

Option A is correct

Answer

B.

Answer

C.

Answer

D.

Question 44

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 45

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

Accepted Answer

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

Answer

0.03

Answer

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

Answer

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

Question 46

Use the Unit Circle to determine the exact value of:

$$ an45\degree-\sin60\degree$$

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 47

Use the Unit Circle to determine the exact value of:

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

Accepted Answer

$$0$$

Answer

$$\frac{1}{4}$$

Answer

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

Answer

$$1$$

Question 48

Use the Unit Circle to determine the exact value of:

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

Accepted Answer

$$-2\sqrt{3}$$

Answer

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

Answer

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

Answer

$$\sqrt{3}$$

Question 49

Use the Unit Circle to determine the exact value of:

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

Accepted Answer

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

Answer

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

Answer

$$-1-\sqrt{6}$$

Answer

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

Question 50

Use the Unit Circle to determine the exact value of:

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

Accepted Answer

-2

Answer

2

Answer

1

Answer

-1

Question 51

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 52

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 53

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 54

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

Accepted Answer

$$y$$

Answer

$$x$$

Answer

$$\frac{x}{y}$$

Answer

$$\frac{y}{x}$$

Question 55

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

Accepted Answer

$$x$$

Answer

Answer

$$\frac{x}{y}$$

Answer

$$\frac{y}{x}$$

Question 56

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

Accepted Answer

$$\frac{y}{x}$$

Answer

$$\frac{y}{r}$$

Answer

$$\frac{x}{r}$$

Answer

$$\frac{r}{y}$$

PreCalculus 11 (NS) Radicals and Trig Review

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