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 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 central angle of $$2$$ radians in a circle of radius $$5$$ meters intercepts an arc of what length?

Accepted Answer

$$10$$ meters

Question 4

What is the area of a sector of a circle with radius $$8 cm $$and central angle $$\frac{\pi}{3}$$ radians?

Accepted Answer

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

Question 5

If the radius of the Earth is approximately $$6400 km$$, what is the north-south distance between two cities at latitudes $$40^{\circ} N $$and $$34^{\circ} N$$?

Accepted Answer

$$670 km$$

Question 6

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

Accepted Answer

$$150^{\circ}$$

Question 7

A rope is wound around a drum of radius $$0.8725 ft $$through an angle of $$39.72^{\circ}. $$How much rope is wound?

Accepted Answer

$$0.605 ft$$

Question 8

If a smaller gear of radius $$2.5 cm $$rotates through $$225^{\circ}$$, through how many degrees will a larger gear of radius $$4.8 cm $$rotate?

Accepted Answer

$$117.2^{\circ}$$

Question 9

What is the exact value of $$\sin\left(\frac{\pi}{6}\right)$$?

Accepted Answer

$$\frac{1}{2}$$

Question 10

Which of the following is the equation of the unit circle?

Accepted Answer

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

Question 11

Find the length of the arc intercepted by a central angle of $$144^{\circ} in a $$circle of radius $$18.2 cm.$$

Accepted Answer

$$45.8 cm$$

Question 12

What is the value of $$\cos(\pi)$$?

Accepted Answer

$$-1$$

Question 13

A sector-shaped field has a radius of $$324 m $$and a central angle of $$15^{\circ}. $$What is the area of the field?

Accepted Answer

$$21,375$$ $$m^2$

Question 14

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 15

Which of the following statements about radians is true?

Accepted Answer

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

Question 16

What is the reference angle for $$210^{\circ}$$?

Accepted Answer

$$30^{\circ}$$

Question 17

If $$\sin(	heta) = \frac{\sqrt{3}}{2}$$ and $$	heta is in $$the second quadrant, what is $$	heta in $$radians?

Accepted Answer

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

Question 18

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

Accepted Answer

$$s = r	heta$$

Question 19

What is the value of $$	an\left(\frac{\pi}{4}ight)$$?

Accepted Answer

$$1$$

Radian Measure and the Unit Circle: Precalculus Study Notes

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