Q: What is the area of a sector of a circle with radius $$r$$ and angle $$\theta (in $$radians)?

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

Question 1

Which of the following best describes a positive angle in standard position?

Accepted Answer

An angle generated by counterclockwise rotation from the positive x-axis.

Question 2

If an angle measures $$300^\circ$$, is it positive or negative, and in which quadrant does its terminal side lie?

Accepted Answer

Positive; Quadrant IV

Question 3

Which of the following pairs of angles are coterminal?

Accepted Answer

$$60^\circ$$ and $$420^\circ$$

Question 4

What is the supplement of a $$70^\circ$$ angle?

Accepted Answer

$$110^\circ$$

Question 5

Which of the following angles does NOT have a complement?

Accepted Answer

$$90^\circ$$

Question 6

Convert $$15^\circ 30' 45'' to $$decimal degrees.

Accepted Answer

$$15.5125^\circ$$

Question 7

What is the formula for the circumference of a circle with radius $$r$$?

Accepted Answer

$$C = 2 \pi r$$

Question 8

Find the area of a sector with $$r = 6$$ and $$	heta = 120^\circ = \frac{2\pi}{3}$$ radians.

Accepted Answer

$$A = 12\pi$$

Question 9

Two cities are both at $$40^\circN $$latitude. One is at $$75^\circW $$longitude, the other at $$85^\circW $$longitude. What is the distance between them? (Earth's radius $$\approx 3960$$ miles)

Accepted Answer

$$530$$ miles

Question 10

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

Accepted Answer

$$D + \frac{M}{60} + \frac{S}{3600}$$

Question 11

If $$\$$theta_1$$ + \$$theta_2$$ = 180^\circ$$, what are $$\$$theta_1$$ and $$\$$theta_2$$ called?

Accepted Answer

Supplementary angles

Question 12

A circle has a radius of $$r$$ and an angle $$	heta in $$radians. What is the formula for the arc length $$s$$?

Accepted Answer

$$s = r	heta$$

Question 13

Which of the following angles is coterminal with $$45^\circ$$?

Accepted Answer

$$405^\circ$$

Question 14

What is the complement of a $$30^\circ$$ angle?

Accepted Answer

$$60^\circ$$

Question 15

Which of the following statements about angles is TRUE?

Accepted Answer

An angle equal to $$180^\circ$$ does not have a supplement.

Question 16

If Tampa is at $$(27.9^\circ N, 82.5^\circ W)$$ and Miami is at $$(25.8^\circ N, 80.2^\circ W)$$, which city is further north and which is further west?

Accepted Answer

Tampa is further north and further west.

Question 17

What is the area of a sector of a circle with radius $$r$$ and angle $$	heta (in $$radians)?

Accepted Answer

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

Question 18

Which of the following is NOT a property of angles in standard position?

Accepted Answer

The terminal side always lies in Quadrant I.

Question 19

If an angle is $$200^\circ$$, which of the following is true?

Accepted Answer

It has neither a complement nor a supplement.

Angles and Radian Measure: Precalculus Study Notes

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