Q: Which of the following is the correct expression for $$\tan(\alpha + \beta)$$?

$$\frac{\tan \alpha + \tan \beta}{1 - \tan \alpha \tan \beta}$$

Question 1

Convert $$135^{\circ} to $$radians. Which of the following is correct?

Accepted Answer

$$\frac{3\pi}{4}$$

Question 2

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

Accepted Answer

$$\pi$$ radians/minute

Question 3

Which of the following is the correct value for $$\sin(60$$^{\circ}$$)$$?

Accepted Answer

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

Question 4

Given $$	an(	heta) = \frac{3}{4}$$ and $$	heta is in $$the first quadrant, what is $$\sin(	heta)$$?

Accepted Answer

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

Question 5

Which of the following is the period of the function $$y = 2\sin(3x)$$?

Accepted Answer

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

Question 6

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

Accepted Answer

$$4$$

Question 7

Solve for $$x in$$ $$2\sin(x) = 1$$ for $$0 \leq x \u003c 2\pi.$$

Accepted Answer

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

Question 8

Which identity is used to simplify $$\sin^2$(x) + \cos^2$(x)$$?

Accepted Answer

$$1$$

Question 9

Given $$\cos(\alpha) = \frac{5}{13}$$ and $$\alpha is in $$quadrant IV, what is $$\sin(\alpha)$$?

Accepted Answer

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

Question 10

Solve the triangle with $$a = 7$$, $$b = 10$$, and $$C = 30$$^{\circ}$$. What is the length of side c$?

Accepted Answer

$$c = \sqrt{7^2$ + 10^2$ - 2 \cdot 7 \cdot 10 \cdot \cos(30$$^{\circ}$$)}$$

Question 11

Convert the point $$(3, 3)$$ from rectangular to polar coordinates.

Accepted Answer

$$(3\sqrt{2}, \frac{\pi}{4})$$

Question 12

Find the product of the complex numbers $$2(\cos 30$$^{\circ}$$ + i\sin 30$$^{\circ}$$)$$ and $$3(\cos 45$$^{\circ}$$ + i\sin 45$$^{\circ}$$) in $$trigonometric form.

Accepted Answer

$$6\left(\cos 75$$^{\circ}$$ + i\sin 75$$^{\circ}$$\right)$$

Question 13

If $$\vec{u} = \langle 2, 3 \rangle$$ and $$\vec{v} = \langle -1, 4 \rangle$$, what is the dot product $$\vec{u} \cdot \vec{v}$$?

Accepted Answer

$$10$$

Question 14

A force of 50 N acts at an angle of $$60^{\circ}$$ above the horizontal. What is the horizontal component of the force?

Accepted Answer

$$50 \cos 60$$^{\circ}$$

Question 15

Which of the following is the correct formula for the area of a triangle given two sides $$a$$, $$b$$ and included angle $$C$$?

Accepted Answer

$$A = \frac{1}{2}ab\sin C$$

Question 16

Find all solutions to $$\cos(2x) = 0$$ for $$0 \leq x \u003c 2\pi.$$

Accepted Answer

$$x = \frac{\pi}{4}, \frac{3\pi}{4}, \frac{5\pi}{4}, \frac{7\pi}{4}$$

Question 17

Given $$\vec{a} = \langle 1, 2, 3 angle$$ and $$\vec{b} = \langle 4, 5, 6 angle$$, what is the cross product $$\vec{a} 	imes \vec{b}$$?

Accepted Answer

$$\langle -3, 6, -3 \rangle$$

Question 18

Which of the following is the correct expression for $$	an(\alpha + \beta)$$?

Accepted Answer

$$\frac{	an \alpha + 	an \beta}{1 - 	an \alpha 	an \beta}$$

Question 19

If $$z = 2(\cos 120$$^{\circ}$$ + i\sin 120$$^{\circ}$$)$$, what is $$z^3 in $$trigonometric form using DeMoivre’s Theorem?

Accepted Answer

$$8\left(\cos 360$$^{\circ}$$ + i\sin 360$$^{\circ}$$\right)$$

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