Q: Which of the following is the correct formula to convert an angle from degrees to radians?

$$\theta_{\text{rad}} = \theta_{\text{deg}} \cdot \frac{\pi}{180}$$

Q: Which of the following is the correct formula for the area $$A of a $$sector with radius $$r$$ and central angle $$\theta (in $$radians)?

$$A = \frac{1}{2} r^2$ \theta$$

Q: Which of the following is NOT a valid way to express a coterminal angle for $$\theta = 120$$^{\circ}$$?

$$\theta = 120$$^{\circ}$$ - 360$$^{\circ}$$ n$$, where $$n is $$any integer

Question 1

Which of the following best describes an angle in standard position?

Accepted Answer

Its vertex is at the origin and its initial side lies along the positive $$x-$$axis.

Question 2

If two angles are coterminal, which of the following must be true?

Accepted Answer

They have the same vertex, initial side, and terminal side.

Question 3

Which of the following is the correct formula to convert an angle from degrees to radians?

Accepted Answer

$$	heta_{	ext{rad}} = 	heta_{	ext{deg}} \cdot \frac{\pi}{180}$$

Question 4

A sector of a circle has a radius of $$7$$ units and a central angle of $$\frac{\pi}{2}$$ radians. What is the area of the sector?

Accepted Answer

$$\frac{49\pi}{4}$$

Question 5

Which of the following points lies on the unit circle?

Accepted Answer

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

Question 6

If an angle measures $$120^{\circ}$$, what is its measure in radians?

Accepted Answer

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

Question 7

A circle has a radius of $$10$$ units. What is the length of the arc subtended by a central angle of $$72^{\circ}$$?

Accepted Answer

Question 8

Which of the following angles is coterminal with $$45^{\circ}$$?

Accepted Answer

$$405^{\circ}$$

Question 9

If the coordinates of a point on the unit circle are $$\left( x, y \right)$$, which equation must always be satisfied?

Accepted Answer

$$x^2$$ + $$y^2 = 1$

Question 10

A central angle in a circle of radius $$r$$ subtends an arc of length $$s. $$Which formula correctly relates $$s$$, $$r$$, and $$	heta (in $$radians)?

Accepted Answer

$$s = r 	heta$$

Question 11

Which of the following pairs of angles are complementary?

Accepted Answer

$$30^{\circ}$$ and $$60^{\circ}$$

Question 12

A circle has a radius of $$6$$ units. What is the area of a sector with a central angle of $$90^{\circ}$$?

Accepted Answer

$$9\pi$$

Question 13

Which of the following is the radian measure of $$225^{\circ}$$?

Accepted Answer

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

Question 14

If an angle is in standard position and its terminal side lies in Quadrant II, which of the following could be its measure?

Accepted Answer

$$135^{\circ}$$

Question 15

A circle has a radius of $$8$$ units. What is the length of the arc subtended by a central angle of $$\frac{3\pi}{4}$$ radians?

Accepted Answer

$$6\pi$$

Question 16

Which of the following is the correct formula for the area $$A of a $$sector with radius $$r$$ and central angle $$	heta (in $$radians)?

Accepted Answer

$$A = \frac{1}{2} r^2$ 	heta$$

Question 17

If an angle measures $$\frac{5\pi}{4}$$ radians, what is its measure in degrees?

Accepted Answer

$$225^{\circ}$$

Question 18

Which of the following is a supplementary pair of angles?

Accepted Answer

$$120^{\circ}$$ and $$60^{\circ}$$

Question 19

A Ferris wheel has a radius of $$20$$ meters. If a passenger travels along an arc of $$\frac{\pi}{3}$$ radians, how far have they traveled?

Accepted Answer

$$\frac{20\pi}{3}$$ meters

Question 20

Which of the following is NOT a valid way to express a coterminal angle for $$	heta = 120$$^{\circ}$$?

Accepted Answer

$$	heta = 120$$^{\circ}$$ - 360$$^{\circ}$$ n$$, where $$n is $$any integer

Angles, Unit Circle, and Radian Measure

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