Q: Which of the following is the correct formula for the area of a sector with radius $$r$$ and central angle $$\theta in $$radians?

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

Question 1

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

Accepted Answer

$$\dfrac{3\pi}{4}$$

Question 2

A sector of a circle has a radius of $$4$$ meters and a central angle of $$60^\circ. $$What is the length of the arc of the sector?

Accepted Answer

$$\dfrac{4\pi}{3}$$ meters

Question 3

Which of the following points lies on the unit circle?

Accepted Answer

$$\left(\dfrac{5}{13},\dfrac{12}{13}\right)$$

Question 4

If $$	an \omega = -2$$ and $$\sin \omega \u003e 0$$, what is the value of $$\sin \omega$$?

Accepted Answer

Question 5

A city at latitude $$52^\circ 30' N $$and another at $$40^\circ 00' N $$are due north-south of each other. If the Earth's radius is $$3960$$ miles, what is the distance between the two cities along the surface of the Earth?

Accepted Answer

$$\approx 834$$ miles

Question 6

Given $$\sec \omega = -\dfrac{5}{3}$$ and $$\sin \omega \u003e 0$$, what is $$\sin \omega$$?

Accepted Answer

Question 7

What is the amplitude and period of the function $$y = -3 \cos(2x)$$?

Accepted Answer

Amplitude: $$3$$, Period: $$\pi$$

Question 8

Find the reference angle for $$250^\circ.$$

Accepted Answer

$$70^\circ$$

Question 9

If $$\sin \omega = -\dfrac{3}{5}$$ and $$\omega is in $$the third quadrant, what is $$\cos \omega$$?

Accepted Answer

$$-\dfrac{4}{5}$$

Question 10

Which equation represents a sine function with amplitude $$5$$, period $$\dfrac{2\pi}{3}$$, and phase shift $$-\dfrac{\pi}{6}$$?

Accepted Answer

$$y = 5 \sin\left(3x - \dfrac{\pi}{2}\right)$$

Question 11

Evaluate $$\cot\left(\dfrac{3\pi}{4}\right).$$

Accepted Answer

$$-1$$

Question 12

A population of deer is modeled by $$N(t) = 450 \sin\left(\dfrac{\pi t}{6}\right) + 1550$$, where $$t is $$years since 2010. What is the population in 2015?

Accepted Answer

$$2000$$

Question 13

Which of the following is a Pythagorean identity?

Accepted Answer

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

Question 14

What is the period of $$y = 	an(2x)$$?

Accepted Answer

$$\dfrac{\pi}{2}$$

Question 15

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

Accepted Answer

$$-\dfrac{\sqrt{17}}{1}$$

Question 16

Which of the following is the correct formula for the area of a sector with radius $$r$$ and central angle $$	heta in $$radians?

Accepted Answer

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

Question 17

What is the value of $$\sin\left(-\dfrac{\pi}{2}\right)$$?

Accepted Answer

$$-1$$

Question 18

The graph of $$y = 2 	an(3x + \dfrac{\pi}{2})$$ has which period and phase shift?

Accepted Answer

Period: $$\dfrac{\pi}{3}$$, Phase shift: $$-\dfrac{\pi}{6}$$

Question 19

Find the equation of the line passing through $$(1,2)$$ and making an angle of $$45^\circ$$ with the positive $$x-$$axis.

Accepted Answer

$$y - 2 = 1(x - 1)$$

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

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