Q: Which of the following is a correct trigonometric identity?

$$\sin^2$\theta + \cos^2$\theta = 1$$

Q: A triangle has sides $$a = 7$$, $$b = 10$$, and angle $$C = 45^\circ. $$What is the area of the triangle?

$$\frac{1}{2} \times 7 \times 10 \times \sin 45^\circ = 35 \times \frac{\sqrt{2}}{2} = 24.75$$

Q: Which of the following is the correct double-angle formula for cosine?

$$\cos(2\theta) = \cos^2$\theta - \sin^2$\theta$$

Question 1

Which of the following best describes the relationship between degrees and radians for measuring angles?

Accepted Answer

One degree is equal to $$\frac{\pi}{180}$$ radians.

Question 2

A Ferris wheel rotates such that a passenger completes one revolution every 2 minutes. If the radius of the wheel is 20 meters, what is the angular velocity in radians per minute?

Accepted Answer

$$\pi$$ radians per minute

Question 3

Which of the following is the correct definition of the sine function on the unit circle?

Accepted Answer

The sine of an angle is the y-coordinate of the point on the unit circle corresponding to that angle.

Question 4

Which of the following is a correct trigonometric identity?

Accepted Answer

$$\sin^2$	heta + \cos^2$	heta = 1$$

Question 5

A sound wave can be modeled by the function $$y = 3\sin(2t + \frac{\pi}{4}). $$What is the amplitude of the wave?

Accepted Answer

3

Question 6

If $$\sin	heta = \frac{1}{2}$$ and $$	heta is in $$the first quadrant, what is $$\cos	heta$$?

Accepted Answer

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

Question 7

Which formula is used to find the area of a triangle given two sides and the included angle?

Accepted Answer

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

Question 8

A triangle has sides $$a = 7$$, $$b = 10$$, and angle $$C = 45^\circ. $$What is the area of the triangle?

Accepted Answer

$$\frac{1}{2} 	imes 7 	imes 10 	imes \sin 45^\circ = 35 	imes \frac{\sqrt{2}}{2} = 24.75$$

Question 9

Which of the following is the correct Law of Sines?

Accepted Answer

$$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$$

Question 10

Which equation represents the Law of Cosines?

Accepted Answer

$$c^2$$ = $$a^2$$ + $$b^2 - 2ab$$\cos C$$

Question 11

Solve for $$x in $$the equation $$2\sin x = 1$$ where $$x is in$$ $$[0, 2\pi].$$

Accepted Answer

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

Question 12

Which of the following is the correct sum formula for sine?

Accepted Answer

$$\sin(A+B) = \sin A \cos B + \cos A \sin B$$

Question 13

Which of the following is the correct double-angle formula for cosine?

Accepted Answer

$$\cos(2	heta) = \cos^2$	heta - \sin^2$	heta$$

Question 14

If $$	an	heta = 3$$ and $$	heta is in $$the second quadrant, what is $$\sin	heta$$?

Accepted Answer

$$-\frac{3}{\sqrt{10}}$$

Question 15

Which of the following is the correct property of logarithms?

Accepted Answer

$$\log_b(xy) = \log_b x + \log_b y$$

Question 16

Solve for $$x$$: $$\log_2$ x = 5$$

Accepted Answer

$$x = 32$$

Question 17

A pendulum swings according to $$y = 4\cos(\omega t)$$, where $$\omega is $$the angular frequency. If the period is 2 seconds, what is $$\omega$$?

Accepted Answer

$$\omega = \pi$$

Question 18

Which of the following is the correct inverse function for cosine?

Accepted Answer

$$\cos$$^{-1}$$ x$$

Trigonometry (MATH 1316) Syllabus and Course Overview – Precalculus Study Guide

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