Question 1

Given a right triangle with legs of length $$3$$ and $$4$$, what is the value of $$\sin(	heta)$$, where $$	heta is $$the angle opposite the side of length $$3$$?

Accepted Answer

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

Question 2

Which of the following is the correct value for $$\cos\left(\frac{\pi}{2}\right)$$?

Accepted Answer

$$0$$

Question 3

If $$	an(	heta) = \frac{5}{12}$$ and $$	heta is in $$the first quadrant, what is $$\sin(	heta)$$?

Accepted Answer

$$\frac{5}{13}$$

Question 4

Which quadrant does the terminal side of an angle of $$225^\circ$$ lie in?

Accepted Answer

Quadrant III

Question 5

What is the period of the function $$y = 2\cos\left(\frac{\pi}{2}x\right)$$?

Accepted Answer

$$4$$

Question 6

If $$\sin(	heta) = -\frac{1}{2}$$ and $$	heta is in $$the third quadrant, what is $$	heta in $$radians?

Accepted Answer

$$\frac{7\pi}{6}$$

Question 7

Which of the following transformations will reflect the graph of $$y = f(x)$$ over the $$x-$$axis?

Accepted Answer

$$y = -f(x)$$

Question 8

Given $$y = 3\sin(x)$$, what is the amplitude of the function?

Accepted Answer

$$3$$

Question 9

If $$\cos(	heta) = 0$$ and $$0 \leq 	heta \u003c 2\pi$$, what are the possible values for $$	heta$$?

Accepted Answer

$$\frac{\pi}{2}, \frac{3\pi}{2}$$

Question 10

A Ferris wheel with a radius of $$10$$ meters makes one complete revolution every $$20$$ seconds. Which equation models the height $$h(t)$$ above the ground of a seat at time $$t$$ seconds, assuming the lowest point is $$0$$ meters?

Accepted Answer

$$h(t) = 10 - 10\cos\left(\frac{\pi}{10}t\right)$$

Question 11

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

Accepted Answer

$$0$$

Question 12

If $$y = f(x)$$ has a period of $$2\pi$$, what is the period of $$y = f(2x)$$?

Accepted Answer

$$\pi$$

Question 13

Which of the following is the correct value for $$\sec\left(\frac{\pi}{3}\right)$$?

Accepted Answer

$$2$$

Question 14

If $$\sin(	heta) = \frac{4}{5}$$ and $$	heta is in $$the second quadrant, what is $$\cos(	heta)$$?

Accepted Answer

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

Question 15

Which transformation shifts the graph of $$y = f(x) to $$the right by $$2$$ units?

Accepted Answer

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

Question 16

If $$y = -2\cos(x)$$, what is the amplitude and the reflection property of the graph?

Accepted Answer

Amplitude is $$2$$, reflected over the $$x-$$axis

Question 17

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

Accepted Answer

$$1$$

Question 18

If $$\sin(	heta) = 0$$ and $$0 \leq 	heta \u003c 2\pi$$, what are the possible values for $$	heta$$?

Accepted Answer

$$0, \pi$$

Question 19

A sound wave can be modeled by $$y = 0.5\sin(440\pi t). $$What is the period of this wave?

Accepted Answer

$$\frac{1}{220}$$

Question 20

If $$y = f(x) is $$vertically stretched by a factor of $$3$$, which equation represents the new function?

Accepted Answer

$$y = 3f(x)$$

Precalculus Study Notes: Trigonometric Functions, Unit Circle, and Graph Transformations

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