Question 1

A Ferris wheel with a radius of 20 meters completes one full revolution every 2 minutes. What is the angular speed of the Ferris wheel in radians per minute?

Accepted Answer

$$\pi$$

Question 2

Convert $$225^\circ to $$radians.

Accepted Answer

$$\frac{5\pi}{4}$$

Question 3

A ladder leans against a wall, forming a $$65^\circ$$ angle with the ground. If the ladder is 10 ft long, how high up the wall does it reach? (Round to two decimal places.)

Accepted Answer

$$10 \sin(65^\circ) \approx 9.06 ft$$

Question 4

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

Accepted Answer

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

Question 5

Evaluate $$\cos\left(\arcsin\left(\frac{3}{5}\right)\right).$$

Accepted Answer

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

Question 6

Which of the following is the period of $$y = 2 \cos\left(\frac{\pi}{3}x\right)$$?

Accepted Answer

$$6$$

Question 7

Find all solutions to $$2\cos(x) - 1 = 0 in$$ $$[0, 2\pi).$$

Accepted Answer

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

Question 8

Simplify $$	an(x)\cos(x).$$

Accepted Answer

$$\sin(x)$$

Question 9

Evaluate $$\sin(75^\circ)$$ using the sum formula.

Accepted Answer

$$\frac{\sqrt{6} + \sqrt{2}}{4}$$

Question 10

If $$\cos(	heta) = -\frac{3}{5}$$ and $$	heta is in $$Quadrant II, what is $$\sin\left(\frac{	heta}{2}ight)$$?

Accepted Answer

$$\frac{1}{\sqrt{5}}$$

Question 11

Let $$\vec{u} = \langle 2, -3 \rangle$$ and $$\vec{v} = \langle -4, 1 \rangle. $$What is $$\vec{u} \cdot \vec{v}$$?

Accepted Answer

$$-5$$

Question 12

Which of the following systems has infinitely many solutions?

Accepted Answer

$$x + 2y = 4$$ and $$2x + 4y = 8$$

Question 13

Find the vector from $$P(1, 2) to$$ $$Q(4, -2) in $$component form.

Accepted Answer

$$\langle 3, -4 \rangle$$

Question 14

Which of the following is the correct amplitude and midline for $$y = -3\sin(x) + 2$$?

Accepted Answer

Amplitude $$3$$, midline $$y = 2$$

Question 15

If $$\vec{a} = \langle 1, 2 angle$$ and $$\vec{b} = \langle -4, 2 angle$$, what is the angle $$	heta$$ between them? (Use $$\cos	heta = \frac{\vec{a} \cdot \vec{b}}{||\vec{a}||\,||\vec{b}||})$$

Accepted Answer

$$\cos$$^{-1}$$\left(\frac{0}{\sqrt{5}\sqrt{20}}\right) = 90^\circ$$

Question 16

Solve the system: $$3x - 2y = 7$$ and $$2x + y = 4.$$

Accepted Answer

$$(2, 0)$$

Question 17

Which of the following is a coterminal angle to $$-\frac{\pi}{4}$$ between $$0$$ and $$2\pi$$?

Accepted Answer

$$\frac{7\pi}{4}$$

Question 18

Which trigonometric functions are positive in Quadrant III?

Accepted Answer

Tangent only

Question 19

If $$\sin(\alpha) = \frac{5}{13}$$ and $$\alpha is in $$Quadrant II, what is $$\cos(\alpha)$$?

Accepted Answer

$$-\frac{12}{13}$$

Question 20

Solve for $$x in$$ $$\sin(2x) = \cos(x)$$ for $$x in$$ $$[0, 2\pi).$$

Accepted Answer

$$x = \frac{\pi}{6}, \frac{5\pi}{6}, \frac{\pi}{2}, \frac{3\pi}{2}$$

Precalculus Study Guide: Trigonometry, Vectors, and Systems of Equations

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