Q: A ladder leans against a wall making an angle of $$\frac{\pi}{3}$$ with the ground. If the ladder is 10 ft long, how high up the wall does it reach?

$$10 \sin\left(\frac{\pi}{3}\right) = 10 \times \frac{\sqrt{3}}{2} = 5\sqrt{3} ft$$

Q: Which of the following is the domain of $$f(x) = \tan(x)$$?

$$x \neq \frac{\pi}{2} + n\pi$$, where $$n$$ \text{ is any integer}$

Question 1

Which of the following is the correct value for $$\sin\left(\frac{\pi}{4}\right)$$?

Accepted Answer

$$\frac{\sqrt{2}}{2}$$

Question 2

Evaluate $$	an\left(\frac{\pi}{3}ight).$$

Accepted Answer

$$\sqrt{3}$$

Question 3

Which of the following is the exact value of $$\cos\left(\frac{\pi}{6}\right)$$?

Accepted Answer

$$\frac{\sqrt{3}}{2}$$

Question 4

If $$\sin(	heta) = \frac{1}{2}$$ and $$0 \leq 	heta \leq \pi$$, what is $$	heta$$?

Accepted Answer

$$\frac{\pi}{6} or$$ $$\frac{5\pi}{6}$$

Question 5

A ladder leans against a wall making an angle of $$\frac{\pi}{3}$$ with the ground. If the ladder is 10 ft long, how high up the wall does it reach?

Accepted Answer

$$10 \sin\left(\frac{\pi}{3}ight) = 10 	imes \frac{\sqrt{3}}{2} = 5\sqrt{3} ft$$

Question 6

Which of the following is the period of the function $$f(x) = \sin(2x)$$?

Accepted Answer

$$\pi$$

Question 7

If $$\cos(	heta) = 0$$, which of the following is a possible value for $$	heta in$$ $$[0, 2\pi]$$?

Accepted Answer

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

Question 8

Simplify $$\sin^2$(x) + \cos^2$(x)$$ for any real $$x.$$

Accepted Answer

$$1$$

Question 9

Which of the following is the range of the function $$f(x) = \cos(x)$$?

Accepted Answer

$$[-1, 1]$$

Question 10

If $$	an(x) = 1$$, what is the general solution for $$x$$?

Accepted Answer

$$x = \frac{\pi}{4} + n\pi$$, where $$n is $$any integer

Question 11

A Ferris wheel has a radius of 20 meters. What is the height above the ground of a seat at an angle $$	heta$$ from the horizontal, if the center is 25 meters above the ground?

Accepted Answer

$$25 + 20\sin(	heta)$$

Question 12

Which of the following is the amplitude of $$f(x) = 3\sin(x)$$?

Accepted Answer

$$3$$

Question 13

Find the exact value of $$\sin(\pi - x) in $$terms of $$\sin(x)$$ and $$\cos(x).$$

Accepted Answer

$$\sin(\pi - x) = \sin(x)$$

Question 14

Which of the following is the domain of $$f(x) = 	an(x)$$?

Accepted Answer

$$x 
eq \frac{\pi}{2} + n\pi$$, where $$n$$ 	ext{ is any integer}$

Question 15

If $$\cos(x) = \frac{1}{2}$$ and $$0 \leq x \u003c 2\pi$$, what are the possible values of $$x$$?

Accepted Answer

$$x = \frac{\pi}{3} or$$ $$x = \frac{5\pi}{3}$$

Question 16

Which of the following is the correct value for $$\sin(0)$$?

Accepted Answer

$$0$$

Question 17

A sound wave can be modeled by $$y = 2\sin(440\pi t)$$, where $$t is $$time in seconds. What is the amplitude and period of the wave?

Accepted Answer

Amplitude: $$2$$, Period: $$\frac{1}{220}$$

Question 18

Which of the following is the correct value for $$\cos(\pi)$$?

Accepted Answer

$$-1$$

Question 19

If $$\sin(x) = \frac{\sqrt{3}}{2}$$ and $$0 \leq x \u003c 2\pi$$, what are the possible values of $$x$$?

Accepted Answer

$$x = \frac{\pi}{3} or$$ $$x = \frac{2\pi}{3}$$

Reference Table of Trigonometric Values and Identities

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