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)?

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

Q: A field is in the shape of a sector with radius 327 m and central angle $$15^{\circ}. $$What is the area of the field? (First convert to radians)

$$\frac{1}{2} \times 327^2$ \times \frac{\pi}{12}$$

Q: Which of the following is the correct formula for converting degrees to radians?

$$\text{radians} = \text{degrees} \times \frac{\pi}{180}$$

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.

Question 2

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

Accepted Answer

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

Question 3

A circle has a radius of 10 cm. What is the length of the arc intercepted by a central angle of $$\frac{\pi}{3}$$ radians?

Accepted Answer

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

Question 4

If two angles are supplementary and one angle measures $$x^{\circ}$$, what is the measure of the other angle?

Accepted Answer

$$180^{\circ}$$ - $$x^{\circ}$$

Question 5

A belt runs a pulley of radius 6 cm at 80 revolutions per minute. What is the angular speed of the pulley in radians per second?

Accepted Answer

$$\frac{8\pi}{3}$$ radians/sec

Question 6

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

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

Question 7

Find the smallest positive angle coterminal with $$-75^{\circ}.$$

Accepted Answer

$$285^{\circ}$$

Question 8

A point on a circle of radius 10 cm rotates with an angular speed of $$\frac{\pi}{4}$$ radians per second. What is the linear speed of the point?

Accepted Answer

$$\frac{10\pi}{4} cm/sec$$

Question 9

Convert $$2.5$$ degrees to degrees, minutes, and seconds.

Accepted Answer

$$2^{\circ} 30$$' 0''$$

Question 10

The latitude of City A is $$52^{\circ} N $$and City B is $$40^{\circ} N. If $$the radius of Earth is 6400 km, what is the north-south distance between the two cities? (Use $$\pi \approx 3.14)$$

Accepted Answer

$$1340 km$$

Question 11

Which of the following is true about coterminal angles?

Accepted Answer

They differ by a multiple of $$360^{\circ}.$$

Question 12

Convert $$\frac{5\pi}{6}$$ radians to degrees.

Accepted Answer

$$150^{\circ}$$

Question 13

A field is in the shape of a sector with radius 327 m and central angle $$15^{\circ}. $$What is the area of the field? (First convert to radians)

Accepted Answer

$$\frac{1}{2} 	imes 327^2$ 	imes \frac{\pi}{12}$$

Question 14

Which of the following is the correct formula for converting degrees to radians?

Accepted Answer

$$	ext{radians} = 	ext{degrees} 	imes \frac{\pi}{180}$$

Question 15

If the sum of two angles is $$90^{\circ}$$, what are these angles called?

Accepted Answer

Complementary

Chapter 9: The Unit Circle and the Functions of Trigonometry – Angles, Arc, and Their Measures

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