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

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

Question 1

Which of the following best describes a quadrantal angle?

Accepted Answer

An angle whose terminal side lies along the x or y axis, such as $$90^\circ$$, $$180^\circ$$, or $$270^\circ.$$

Question 2

A central angle in a circle intercepts an arc equal in length to the radius of the circle. What is the measure of this angle in radians?

Accepted Answer

$$1$$ radian

Question 3

Convert $$135^\circ to $$radians.

Accepted Answer

$$\dfrac{3\pi}{4}$$ radians

Question 4

If two angles are complementary, what is the sum of their measures?

Accepted Answer

$$90^\circ$$

Question 5

A circle has a radius of $$10 cm. $$What is the length of the arc intercepted by a central angle of $$60^\circ$$?

Accepted Answer

$$\dfrac{10\pi}{3} cm$$

Question 6

Convert $$2$$ radians to degrees.

Accepted Answer

$$114.59^\circ$$

Question 7

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

Accepted Answer

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

Question 8

A satellite travels in a circular orbit with a radius of $$8000 km $$and completes one revolution in $$4$$ hours. What is its angular speed in radians per hour?

Accepted Answer

$$\dfrac{2\pi}{4}$$ radians/hour

Question 9

Which of the following is NOT true about coterminal angles?

Accepted Answer

Coterminal angles always have the same measure.

Question 10

Convert $$74^\circ 8' 14'' to $$decimal degrees.

Accepted Answer

$$74.1372^\circ$$

Question 11

A field is shaped like a sector of a circle with radius $$50 m $$and central angle $$120^\circ. $$What is the area of the field?

Accepted Answer

$$4363.32 m$^2$$

Question 12

Which of the following best describes an obtuse angle?

Accepted Answer

An angle greater than $$90^\circ$$ but less than $$180^\circ.$$

Question 13

A wheel rotates $$540^\circ. $$How many radians has it rotated?

Accepted Answer

$$3\pi$$ radians

Question 14

If the sum of two angles is $$180^\circ$$, what are they called?

Accepted Answer

Supplementary angles

Question 15

What is the linear speed $$v of a $$point on a circle of radius $$r$$ rotating at angular speed $$\omega$$?

Accepted Answer

$$v = r\omega$$

Question 16

Convert $$34.817^\circ to $$degrees, minutes, and seconds.

Accepted Answer

$$34^\circ 49' 1''$$

Question 17

Which of the following is the correct formula for arc length $$s$$ intercepted by a central angle $$	heta (in $$radians) in a circle of radius $$r$$?

Accepted Answer

$$s = r	heta$$

Question 18

A right angle is defined as:

Accepted Answer

An angle that is exactly $$90^\circ.$$

Question 19

A ray is defined as:

Accepted Answer

The portion of a line that starts at one point and continues through another.

Question 20

What is the degree measure of one minute ($$1'$$)?

Accepted Answer

$$\dfrac{1}{60}^\circ$$

Angles, Arcs, and Their Measures: Foundations of Trigonometry

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