Q: If $$\theta$$ and $$\phi$$ are coterminal angles, which of the following must be true?

$$\theta - \phi is a $$multiple of $$360^\circ or$$ $$2\pi$$

Question 1

A circle has a radius of $$10$$ meters. What is the length of the arc subtended by a central angle of $$72^\circ$$? (Use $$\pi$$ for $$\omega.)$$

Accepted Answer

$$4\pi$$ meters

Question 2

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

Accepted Answer

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

Question 3

Which of the following points lies on the unit circle?

Accepted Answer

$$(\frac{3}{5}, \frac{4}{5})$$

Question 4

If $$\sec \omega = -\frac{4}{7}$$ and $$\sin \omega \u003c 0$$, what is $$\sin \omega$$?

Accepted Answer

$$-\frac{\sqrt{33}}{7}$$

Question 5

A city at latitude $$52^\circ 30' N is $$due north of a city at latitude $$40^\circ 10' N. If $$the Earth's radius is $$3960$$ miles, what is the distance between the two cities along the surface of the Earth?

Accepted Answer

$$857$$ miles

Question 6

Given $$	an \omega = -2$$ and $$\sin \omega \u003e 0$$, what is $$\cos \omega$$?

Accepted Answer

$$-\frac{1}{\sqrt{5}}$$

Question 7

Find the amplitude and period of $$y = -4 \cos(7x).$$

Accepted Answer

Amplitude: $$4$$, Period: $$\frac{2\pi}{7}$$

Question 8

What is the reference angle for $$500^\circ$$?

Accepted Answer

$$140^\circ$$

Question 9

If $$\cot \omega = 4$$ and $$\csc \omega \u003c 0$$, what is $$\csc \omega$$?

Accepted Answer

$$-\frac{\sqrt{17}}{5}$$

Question 10

A population of deer is modeled by $$N(t) = 450 \sin\left(\frac{\pi t}{6}\right) + 1550$$, where $$t is $$years since 2010. What is the population in 2018?

Accepted Answer

$$2000$$

Question 11

Which equation represents a sine function with amplitude $$3$$, period $$\frac{\pi}{2}$$, and phase shift $$-\frac{\pi}{4}$$?

Accepted Answer

$$y = 3 \sin\left(4x + \pi\right)$$

Question 12

Evaluate $$\sin\left(\frac{\pi}{2}\right).$$

Accepted Answer

$$1$$

Question 13

Given the point $$(-1, -2)$$, what is $$	an \omega$$ for the angle in standard position with terminal side at this point?

Accepted Answer

$$2$$

Question 14

Which of the following is the correct Pythagorean identity?

Accepted Answer

$$\sin^2$ \omega + \cos^2$ \omega = 1$$

Question 15

What is the period of $$y = 2 	an(3x + \frac{\pi}{2})$$?

Accepted Answer

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

Question 16

If $$	heta$$ and $$\phi$$ are coterminal angles, which of the following must be true?

Accepted Answer

$$	heta - \phi is a $$multiple of $$360^\circ or$$ $$2\pi$$

Question 17

Convert $$110.433^\circ to $$degrees, minutes, and seconds.

Accepted Answer

$$110^\circ 25' 59''$$

Question 18

Which of the following is the correct formula for the area of a sector of a circle with radius $$r$$ and central angle $$\epsilon (in $$radians)?

Accepted Answer

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

Question 19

If $$	an \omega = \frac{3}{4}$$ and $$\omega is in $$the first quadrant, what is $$\sin \omega$$?

Accepted Answer

$$\frac{3}{5}$$

Precalculus Study Notes: Angles, Trigonometric Functions, and Their Graphs

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