Q: Given a right triangle where one acute angle is $$\theta$$ and the side opposite $$\theta is 7 $$units while the hypotenuse is 25 units, what is $$\sin \theta$$?

$$\sin \theta = \dfrac{7}{25}$$

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

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

Q: Which equation expresses the double-angle identity for cosine?

$$\cos 2\theta = 2\cos^2$ \theta - 1$$

Q: Which of the following is the correct half-angle identity for sine?

$$\sin \dfrac{\theta}{2} = \pm \sqrt{\dfrac{1 - \cos \theta}{2}}$$

Q: Which of the following is the correct sum identity for tangent?

$$\tan(\alpha + \beta) = \dfrac{\tan \alpha + \tan \beta}{1 - \tan \alpha \tan \beta}$$

Question 1

Given a right triangle where one acute angle is $$	heta$$ and the side opposite $$	heta is 7 $$units while the hypotenuse is 25 units, what is $$\sin 	heta$$?

Accepted Answer

$$\sin 	heta = \dfrac{7}{25}$$

Question 2

If $$	an \alpha = 3$$ and $$\alpha is in $$Quadrant II, what is $$\sin \alpha$$?

Accepted Answer

Question 3

Convert $$150^\circ to $$radians.

Accepted Answer

$$\dfrac{5\pi}{6}$$

Question 4

A Ferris wheel with a radius of 20 meters makes one full revolution every 2 minutes. What is the linear speed of a seat on the edge in meters per minute?

Accepted Answer

$$40\pi m/$$min

Question 5

Which of the following is a fundamental trigonometric identity?

Accepted Answer

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

Question 6

Given $$\sin x = \dfrac{5}{13}$$ and $$x is in $$Quadrant II, find $$\cos x.$$

Accepted Answer

$$-\dfrac{12}{13}$$

Question 7

Which equation expresses the double-angle identity for cosine?

Accepted Answer

$$\cos 2	heta = 2\cos^2$ 	heta - 1$$

Question 8

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

Accepted Answer

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

Question 9

Given $$\sin(\alpha + \beta) = \sin \alpha \cos \beta + \cos \alpha \sin \beta$$, what is $$\sin(75^\circ)$$ using $$45^\circ$$ and $$30^\circ$$?

Accepted Answer

$$\sin(75^\circ) = \sin(45^\circ + 30^\circ) = \sin 45^\circ \cos 30^\circ + \cos 45^\circ \sin 30^\circ$$

Question 10

A ladder leans against a wall making a $$65^\circ$$ angle with the ground. If the foot of the ladder is 4 meters from the wall, how long is the ladder?

Accepted Answer

$$\dfrac{4}{\cos 65^\circ}$$

Question 11

If $$\cos 	heta = -\dfrac{3}{5}$$ and $$	heta is in $$Quadrant III, what is $$\sin 	heta$$?

Accepted Answer

$$-\dfrac{4}{5}$$

Question 12

Which of the following is the correct Law of Sines?

Accepted Answer

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

Question 13

Find the amplitude of the function $$y = 3 \sin(2x - \pi).$$

Accepted Answer

3

Question 14

If $$\sin 	heta = \dfrac{1}{2}$$ and $$0 \u003c 	heta \u003c \pi$$, what are the possible values for $$	heta$$?

Accepted Answer

$$\dfrac{\pi}{6}, \dfrac{5\pi}{6}$$

Question 15

Which of the following is the correct half-angle identity for sine?

Accepted Answer

$$\sin \dfrac{	heta}{2} = \pm \sqrt{\dfrac{1 - \cos 	heta}{2}}$$

Question 16

A rotating object has an angular speed of $$6$$ radians per second and a radius of $$0.5$$ meters. What is its linear speed?

Accepted Answer

$$3 m/s$$

Question 17

If $$	an 	heta = -1$$ and $$	heta is in $$Quadrant II, what is $$	heta$$?

Accepted Answer

$$\dfrac{3\pi}{4}$$

Question 18

Which of the following is the correct sum identity for tangent?

Accepted Answer

$$	an(\alpha + \beta) = \dfrac{	an \alpha + 	an \beta}{1 - 	an \alpha 	an \beta}$$

Question 19

Given $$\sin x = 0.6$$ and $$x is in $$Quadrant I, what is $$\cos x$$?

Accepted Answer

$$0.8$$

Math 1316 Trigonometry: Course Syllabus and Topic Overview

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