Q: Which of the following correctly expresses the sine of an angle $$\theta$$ using the unit circle definition?

$$\sin(\theta) = \text{y-coordinate on the unit circle at angle } \theta$$

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

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

Q: If $$\cos(\theta) = -\frac{1}{2}$$ and $$0 \leq \theta \u003c 2\pi$$, what are the possible values of $$\theta$$?

$$\theta = \frac{2\pi}{3}, \frac{4\pi}{3}$$

Q: Which of the following is the correct relationship for the sine of a negative angle?

$$\sin(-\theta) = -\sin(\theta)$$

Q: A Ferris wheel with a radius of 20 meters rotates such that a rider travels through an angle of $$\frac{5\pi}{6}$$ radians. What is the distance traveled by the rider along the wheel?

$$\frac{5\pi}{6} \times 20 = \frac{100\pi}{6}$$ meters

Q: Solve for $$\theta if$$ $$\tan^2$(\theta) = 3$$ and $$0 \leq \theta \u003c 2\pi.$$

$$\theta = \frac{\pi}{3}, \frac{2\pi}{3}, \frac{4\pi}{3}, \frac{5\pi}{3}$$

Q: If $$\cos(\theta) = 0$$, what are the possible values of $$\theta in$$ $$0 \leq \theta \u003c 2\pi$$?

$$\theta = \frac{\pi}{2}, \frac{3\pi}{2}$$

Q: Which of the following is the correct identity for $$\tan(-\theta)$$?

$$\tan(-\theta) = -\tan(\theta)$$

Question 1

Which of the following correctly expresses the sine of an angle $$	heta$$ using the unit circle definition?

Accepted Answer

$$\sin(	heta) = 	ext{y-coordinate on the unit circle at angle } 	heta$$

Question 2

If $$	heta = 150^\circ$$, which of the following statements about $$\sin(	heta)$$ and $$\cos(	heta) is $$true?

Accepted Answer

$$\sin(150^\circ) is $$positive and $$\cos(150^\circ) is $$negative

Question 3

Given $$	an(	heta) = -\frac{3}{4}$$ and $$\sin(	heta) \u003e 0$$, in which quadrant does $$	heta$$ lie?

Accepted Answer

Quadrant II

Question 4

Which of the following is a correct Pythagorean identity?

Accepted Answer

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

Question 5

Evaluate $$\sin(420^\circ).$$

Accepted Answer

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

Question 6

If $$\cos(	heta) = -\frac{1}{2}$$ and $$0 \leq 	heta \u003c 2\pi$$, what are the possible values of $$	heta$$?

Accepted Answer

$$	heta = \frac{2\pi}{3}, \frac{4\pi}{3}$$

Question 7

Which trigonometric functions are always positive in Quadrant IV?

Accepted Answer

Cosine and secant

Question 8

Given $$	an(	heta) = \frac{5}{12}$$ and $$	heta is in $$Quadrant III, what is $$\sin(	heta)$$?

Accepted Answer

$$-\frac{5}{13}$$

Question 9

Which of the following is the correct relationship for the sine of a negative angle?

Accepted Answer

$$\sin(-	heta) = -\sin(	heta)$$

Question 10

If $$\cos(	heta) = 0.8463$$ and $$0 \leq 	heta \u003c 2\pi$$, what are the two possible values of $$	heta ($$rounded to 4 decimal places)?

Accepted Answer

$$	heta = 0.5667, 5.7165$$

Question 11

A Ferris wheel with a radius of 20 meters rotates such that a rider travels through an angle of $$\frac{5\pi}{6}$$ radians. What is the distance traveled by the rider along the wheel?

Accepted Answer

$$\frac{5\pi}{6} 	imes 20 = \frac{100\pi}{6}$$ meters

Question 12

Which of the following is the correct expanded definition of $$\sin(	heta)$$ for a circle of radius $$r$$ centered at the origin?

Accepted Answer

$$\sin(	heta) = \frac{y}{r}$$

Question 13

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

Accepted Answer

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

Question 14

Which of the following is true about the signs of trigonometric functions in Quadrant III?

Accepted Answer

Tangent and cotangent are positive; sine, cosine, secant, and cosecant are negative

Question 15

Solve for $$	heta if$$ $$	an^2$(	heta) = 3$$ and $$0 \leq 	heta \u003c 2\pi.$$

Accepted Answer

$$	heta = \frac{\pi}{3}, \frac{2\pi}{3}, \frac{4\pi}{3}, \frac{5\pi}{3}$$

Question 16

If $$\cos(	heta) = 0$$, what are the possible values of $$	heta in$$ $$0 \leq 	heta \u003c 2\pi$$?

Accepted Answer

$$	heta = \frac{\pi}{2}, \frac{3\pi}{2}$$

Question 17

Which of the following is the correct identity for $$	an(-	heta)$$?

Accepted Answer

$$	an(-	heta) = -	an(	heta)$$

Question 18

Given $$\cot(	heta) = \frac{1}{2}$$ and $$\sin(	heta) \u003c 0$$, what is the value of $$\cos(	heta)$$?

Accepted Answer

$$-\frac{\sqrt{5}}{\sqrt{1+4}} = -\frac{2}{\sqrt{5}}$$

Question 19

If $$\sin(	heta) = -\frac{1}{2}$$ and $$	heta is in $$Quadrant IV, what is $$	heta in $$radians?

Accepted Answer

$$	heta = \frac{11\pi}{6}$$

Trigonometric Functions: Definitions, Properties, and Applications

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