Q: A Ferris wheel with a radius of $$10$$ meters completes one revolution every $$30$$ seconds. What is the linear speed of a seat on the edge of the wheel?

$$\frac{2\pi \times 10}{30} = \frac{2\pi}{3}$$ meters/second

Q: The latitude of City A is $$40^{\circ} N $$and City B is $$50^{\circ} N. If $$both cities are due north-south of each other and the Earth's radius is $$3960$$ miles, what is the distance between them along the surface? (Use $$\theta = 10$$^{\circ}$$, convert to radians first)

$$3960 \times \frac{\pi}{18} \approx 691$$ miles

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)?

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

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 coincides with the positive x-axis.

Question 2

Convert $$135.75^{\circ} to $$degrees, minutes, and seconds.

Accepted Answer

$$135^{\circ} 45$$' 0''$$

Question 3

A central angle of $$2$$ radians in a circle of radius $$5$$ meters subtends an arc. What is the length of the arc?

Accepted Answer

$$10$$ meters

Question 4

Convert $$120^{\circ} to $$radians.

Accepted Answer

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

Question 5

A circle has a radius of $$8 cm. $$What is the area of a sector formed by a central angle of $$60^{\circ}$$? (Round to two decimal places)

Accepted Answer

$$33.51 cm$^2$$

Question 6

A Ferris wheel with a radius of $$10$$ meters completes one revolution every $$30$$ seconds. What is the linear speed of a seat on the edge of the wheel?

Accepted Answer

$$\frac{2\pi 	imes 10}{30} = \frac{2\pi}{3}$$ meters/second

Question 7

If an object moves along a circle of radius $$r$$ and travels a distance $$s in $$time $$t$$, what is the formula for its linear speed $$v$$?

Accepted Answer

$$v = \frac{s}{t}$$

Question 8

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

Accepted Answer

$$150^{\circ}$$

Question 9

The latitude of City A is $$40^{\circ} N $$and City B is $$50^{\circ} N. If $$both cities are due north-south of each other and the Earth's radius is $$3960$$ miles, what is the distance between them along the surface? (Use $$	heta = 10$$^{\circ}$$, convert to radians first)

Accepted Answer

$$3960 	imes \frac{\pi}{18} \approx 691$$ miles

Question 10

A child spins a rock at the end of a $$2-$$foot rope at $$180$$ revolutions per minute. What is the angular speed $$\omega in $$radians per minute?

Accepted Answer

$$360\pi$$ radians/minute

Question 11

Which of the following is a quadrantal angle?

Accepted Answer

$$270^{\circ}$$

Question 12

What is the area of a sector of a circle with radius $$6$$ meters and central angle $$\frac{\pi}{4}$$ radians?

Accepted Answer

$$9\pi$$ square meters

Question 13

Convert $$72^{\circ} 18$$' 0''$$ to decimal degrees. (Round to four decimal places)

Accepted Answer

$$72.3000^{\circ}$$

Question 14

If an object moves with angular speed $$\omega on a $$circle of radius $$r$$, what is the formula for its linear speed $$v$$?

Accepted Answer

$$v = r\omega$$

Question 15

Which of the following angles lies in quadrant II?

Accepted Answer

$$135^{\circ}$$

Question 16

A central angle of $$	heta$$ radians in a circle of radius $$r$$ subtends an arc of length $$s. $$Which equation is correct?

Accepted Answer

$$s = r	heta$$

Question 17

Convert $$-\frac{\pi}{3}$$ radians to degrees.

Accepted Answer

$$-60^{\circ}$$

Question 18

A circle has a radius of $$10$$ meters. What is the length of the arc subtended by a central angle of $$\frac{\pi}{2}$$ radians?

Accepted Answer

$$5\pi$$ meters

Question 19

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

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

Angles, Arc Length, and Circular Motion – Precalculus Chapter 5 Study Notes

Guida di studio - Domande di pratica

Study guide - Flashcard