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: 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 radian?

Accepted Answer

An angle that intercepts an arc equal in length to the radius of the circle.

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

Find the area of a sector with radius 8 m and central angle $$60^{\circ}.$$

Accepted Answer

$$\frac{32\pi}{3} m$^2$$

Question 5

If the latitude of City A is $$50^{\circ} N $$and City B is $$40^{\circ} N$$, and the radius of Earth is 6371 km, what is the north-south distance between the two cities?

Accepted Answer

$$1111.95 km$$

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

On the unit circle, what are the coordinates of the point corresponding to an angle of $$\frac{\pi}{6}$$?

Accepted Answer

$$\left( \frac{\sqrt{3}}{2}, \frac{1}{2} \right)$$

Question 8

If $$\sin s = 0.5$$ and $$s is in $$the interval $$[0, \pi]$$, what is $$s$$?

Accepted Answer

$$\frac{\pi}{6}$$

Question 9

A pulley with a radius of 6 cm rotates at 80 revolutions per minute. What is its angular speed in radians per second?

Accepted Answer

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

Question 10

A satellite orbits Earth at a distance of 1600 km above the surface. If the radius of Earth is 6400 km, what is the radius of the satellite's orbit?

Accepted Answer

$$8000 km$$

Question 11

If a point moves along a circle of radius $$r$$ and traces an arc of length $$s in $$time $$t$$, what is the formula for its linear speed $$v$$?

Accepted Answer

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

Question 12

Which of the following statements about radians is TRUE?

Accepted Answer

Radians are a pure number, not a unit like degrees.

Question 13

A rope is wound around a drum of radius $$0.8725 ft $$through an angle of $$39.72^{\circ}. $$How much rope is wound? (Give your answer in feet, rounded to 2 decimal places.)

Accepted Answer

0.61 ft

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 $$\cos s = 0.9685$$ and $$s is in$$ $$[0, \frac{\pi}{2}]$$, what is the approximate value of $$s (in $$radians)?

Accepted Answer

0.25

Question 16

Which of the following is NOT a property of the unit circle?

Accepted Answer

Its radius is always 2 units.

Question 17

A sector of a circle has an area of $$20\pi m$^2$$ and a radius of 10 m. What is the measure of the central angle in radians?

Accepted Answer

2

Question 18

If a point on a circle of radius 5 m moves with an angular speed of $$2$$ radians per second, what is its linear speed?

Accepted Answer

10 m/s

Question 19

Which of the following is the correct relationship between linear speed $$v$$, radius $$r$$, and angular speed $$\omega$$?

Accepted Answer

$$v = r \omega$$

Question 20

If $$	an s = 1$$ and $$s is in$$ $$[0, \pi]$$, what is $$s$$?

Accepted Answer

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

Radian Measure and the Unit Circle: Precalculus Study Notes

Guida di studio - Domande di pratica

Study guide - Flashcard