Q: A Ferris wheel is 50 ft tall. After 12 seconds, the wheel has rotated 200°. What is the average angular speed in radians per second?

$$\frac{200 \times \pi}{180 \times 12}$$

Q: Rewrite the system as an augmented matrix: $$2x + 7y = 12$$, $$3x + 4y = 11.$$

$$\begin{bmatrix} 2 & 7 & | & 12 \\ 3 & 4 & | & 11 \end{bmatrix}$$

Q: Which of the following is the correct formula for converting degrees to radians?

$$\text{radians} = \text{degrees} \times \frac{\pi}{180}$$

Question 1

A Ferris wheel is 50 ft tall. After 12 seconds, the wheel has rotated 200°. What is the average angular speed in radians per second?

Accepted Answer

$$\frac{200 	imes \pi}{180 	imes 12}$$

Question 2

Given $$	an(	heta) = 2$$ and $$0 \u003c 	heta \u003c \frac{\pi}{2}$$, use the fundamental identities to find $$\sin(	heta).$$

Accepted Answer

$$\frac{2}{\sqrt{5}}$$

Question 3

Suppose $$\sin(2	heta) = \frac{4}{5}$$ with $$90^\circ \u003c 2	heta \u003c 180^\circ. $$What is $$\sin(	heta)$$?

Accepted Answer

$$\frac{2}{\sqrt{10}}$$

Question 4

Find the coterminal angle of $$	heta = -495^\circ$$ between $$0^\circ$$ and $$360^\circ.$$

Accepted Answer

$$225^\circ$$

Question 5

If $$	heta = 12^\circ$$ and is in Quadrant II, which trigonometric function will be positive?

Accepted Answer

$$\sin(	heta)$$

Question 6

Suppose the point $$\left(\frac{3}{5}, yight) is on $$the unit circle with associated angle $$	heta. $$What is $$y if$$ $$	heta is in $$Quadrant II?

Accepted Answer

$$-\frac{4}{5}$$

Question 7

A standing firetruck shoots water at a $$120^\circ$$ angle. If the fan can be felt up to 10 ft away, what is the total area in which the fan can be felt?

Accepted Answer

$$\frac{1}{3} \pi (10)^2$

Question 8

Evaluate $$\arccos\left(-\frac{1}{2}\right) in $$degrees.

Accepted Answer

$$120^\circ$$

Question 9

Find the partial fraction decomposition for $$\frac{2x+1}{(x+1)(x+2)}.$$

Accepted Answer

$$\frac{-1}{x+1} + \frac{3}{x+2}$$

Question 10

Given $$f(x) = \cos$$^{-1}$$(2x - 1)$$, what is the domain of $$f^{-1}(x$$)$$?

Accepted Answer

$$[0, \pi]$$

Question 11

Rewrite the system as an augmented matrix: $$2x + 7y = 12$$, $$3x + 4y = 11.$$

Accepted Answer

$$\begin{bmatrix} 2 & 7 & | & 12 \ 3 & 4 & | & 11 \end{bmatrix}$$

Question 12

If $$	an(	heta) = -\sqrt{3}$$ and $$\pi \u003c 	heta \u003c \frac{3\pi}{2}$$, what is $$\sin(	heta)$$?

Accepted Answer

$$-\frac{1}{2}$$

Question 13

Which of the following is the correct formula for linear speed $$v$$?

Accepted Answer

$$v = r \omega$$

Question 14

If $$\cos(	heta) = -\frac{1}{2}$$ and $$	heta is in $$Quadrant III, what is $$	heta in $$degrees?

Accepted Answer

$$240^\circ$$

Question 15

Solve the system using substitution: $$x + y = 2$$, $$2x - y = 1.$$

Accepted Answer

$$x = 1, y = 1$$

Question 16

Which of the following is the correct expression for the reference angle of $$-495^\circ$$?

Accepted Answer

$$45^\circ$$

Question 17

If $$\sin(	heta) = \frac{3}{5}$$ and $$	heta is in $$Quadrant II, what is $$\cos(	heta)$$?

Accepted Answer

$$-\frac{4}{5}$$

Question 18

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

Accepted Answer

$$\pi$$

Question 19

Which of the following is the correct formula for converting degrees to radians?

Accepted Answer

$$	ext{radians} = 	ext{degrees} 	imes \frac{\pi}{180}$$

Precalculus Study Guide: Trigonometric Functions, Analytic Trigonometry, and Applications

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