Q: Which of the following correctly converts $$40^\circ to $$radians?

$$40 \times \frac{\pi}{180} = \frac{2\pi}{9}$$

Q: A circle has a radius of $$5$$ meters. What is the area of a sector with a central angle of $$60^\circ$$?

$$\frac{1}{6} \pi \times 25 = \frac{25\pi}{6}$$

Q: Charlotte is at $$32^\circ 54' N $$and Pittsburgh is at $$40^\circ 30' N. If $$the Earth's radius is $$3960$$ miles, what is the distance between the cities along the surface?

$$3960 \times \left(\frac{40.5 - 32.9}{360} \times 2\pi\right) \approx 575$$ miles

Q: Which of the following is a correct Pythagorean identity?

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

Q: The population of deer in a region is modeled by $$N(t) = 450 \sin\left(\frac{\pi t}{6}\right) + 1550$$, where $$t = 0 is 2010. $$What is the population in 2012?

$$N(2) = 450 \sin\left(\frac{\pi \times 2}{6}\right) + 1550 = 450 \sin\left(\frac{\pi}{3}\right) + 1550 = 450 \times \frac{\sqrt{3}}{2} + 1550 \approx 1942$$

Question 1

Which of the following correctly converts $$40^\circ to $$radians?

Accepted Answer

$$40 	imes \frac{\pi}{180} = \frac{2\pi}{9}$$

Question 2

A circle has a radius of $$5$$ meters. What is the area of a sector with a central angle of $$60^\circ$$?

Accepted Answer

$$\frac{1}{6} \pi 	imes 25 = \frac{25\pi}{6}$$

Question 3

Charlotte is at $$32^\circ 54' N $$and Pittsburgh is at $$40^\circ 30' N. If $$the Earth's radius is $$3960$$ miles, what is the distance between the cities along the surface?

Accepted Answer

$$3960 	imes \left(\frac{40.5 - 32.9}{360} 	imes 2\piight) \approx 575$$ miles

Question 4

Which of the following points lies on the unit circle?

Accepted Answer

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

Question 5

Given the point $$\left(\frac{6}{7}, \frac{13}{7}\right)$$, is it on the unit circle?

Accepted Answer

No, because $$\left(\frac{6}{7}\$$right)^2$$ + \left(\frac{13}{7}\$$right)^2$$ = \frac{36}{49} + \frac{169}{49} = \frac{205}{49} 
eq 1$$

Question 6

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

Accepted Answer

$$-\frac{3}{7}$$

Question 7

If $$	an 	heta = -2$$ and $$\sin 	heta \u003e 0$$, which quadrant is $$	heta in$$?

Accepted Answer

Quadrant II

Question 8

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

Accepted Answer

$$140^\circ$$

Question 9

Which of the following is the correct period for $$y = 3 \sin(4x)$$?

Accepted Answer

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

Question 10

What is the amplitude of $$y = -4 \cos x$$?

Accepted Answer

$$4$$

Question 11

What is the phase shift of $$y = 3 \sin(4x + \pi)$$?

Accepted Answer

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

Question 12

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

Accepted Answer

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

Question 13

Which of the following is a correct Pythagorean identity?

Accepted Answer

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

Question 14

What is $$\sin(\frac{\pi}{2})$$?

Accepted Answer

$$1$$

Question 15

The population of deer in a region is modeled by $$N(t) = 450 \sin\left(\frac{\pi t}{6}\right) + 1550$$, where $$t = 0 is 2010. $$What is the population in 2012?

Accepted Answer

$$N(2) = 450 \sin\left(\frac{\pi 	imes 2}{6}ight) + 1550 = 450 \sin\left(\frac{\pi}{3}ight) + 1550 = 450 	imes \frac{\sqrt{3}}{2} + 1550 \approx 1942$$

Question 16

What is the equation of the line passing through $$(2, 5)$$ and making an angle of $$60^\circ$$ with the positive $$x-$$axis?

Accepted Answer

$$y - 5 = \sqrt{3}(x - 2)$$

Question 17

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 18

If $$	an 	heta = \frac{3}{4}$$ and $$	heta is in $$Quadrant III, what is $$\sin 	heta$$?

Accepted Answer

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

Question 19

What is the period of $$y = -4 \cos(7x)$$?

Accepted Answer

$$\frac{2\pi}{7}$$

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

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