Q: Which trigonometric functions are always positive in Quadrant II?

$$\sin \theta$$ and $$\csc \theta$$

Q: Which of the following is true for coterminal angles $$\theta$$ and $$\theta + 2\pi k ($$where $$k is $$any integer)?

$$\sin(\theta + 2\pi k) = \sin \theta$$

Q: Which of the following best describes a reference angle?

The acute angle formed by the terminal side of $$\theta$$ and the x-axis

Question 1

Given the point $$(12, -5) on $$the terminal side of an angle $$	heta$$, what is $$\sin 	heta$$?

Accepted Answer

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

Question 2

Which of the following angles is coterminal with $$420^\circ$$?

Accepted Answer

$$60^\circ$$

Question 3

If $$	heta = 3\pi$$, what is $$\cos 	heta$$?

Accepted Answer

$$-1$$

Question 4

Which trigonometric functions are always positive in Quadrant II?

Accepted Answer

$$\sin 	heta$$ and $$\csc 	heta$$

Question 5

Find the reference angle for $$-45^\circ.$$

Accepted Answer

$$45^\circ$$

Question 6

If $$\sin 	heta  0$$, in which quadrant does $$	heta$$ lie?

Accepted Answer

Quadrant IV

Question 7

What is the value of $$	an 0$$?

Accepted Answer

$$0$$

Question 8

Which of the following is true for coterminal angles $$	heta$$ and $$	heta + 2\pi k ($$where $$k is $$any integer)?

Accepted Answer

$$\sin(	heta + 2\pi k) = \sin 	heta$$

Question 9

If $$\cos 	heta = -\frac{2}{5}$$ and $$\frac{\pi}{2} \u003c 	heta \u003c \pi$$, what is $$\sin 	heta$$?

Accepted Answer

$$\frac{\sqrt{21}}{5}$$

Question 10

A real-world application: A ramp rises 3 meters vertically and runs 4 meters horizontally. What is $$\sin 	heta$$, where $$	heta is $$the angle the ramp makes with the ground?

Accepted Answer

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

Question 11

Find the exact value of $$\cos 135^\circ$$ using a reference angle.

Accepted Answer

$$-\frac{\sqrt{2}}{2}$$

Question 12

If $$	an 	heta = 3$$ and $$\cos 	heta \u003c 0$$, what is $$\sin 	heta$$?

Accepted Answer

$$\frac{3}{\sqrt{10}} (in $$Quadrant II, positive)

Question 13

Which of the following is NOT defined for $$	heta = 90^\circ$$?

Accepted Answer

$$	an 	heta$$

Question 14

If $$	heta = 600^\circ$$, what is the reference angle?

Accepted Answer

$$60^\circ$$

Question 15

Given $$\sin 	heta = -\frac{5}{13}$$ and $$	heta is in $$Quadrant IV, what is $$\cos 	heta$$?

Accepted Answer

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

Question 16

Which of the following best describes a reference angle?

Accepted Answer

The acute angle formed by the terminal side of $$	heta$$ and the x-axis

Question 17

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

Accepted Answer

$$315^\circ$$

Question 18

Which of the following is true for all quadrantal angles?

Accepted Answer

At least one trigonometric function is not defined

Question 19

If $$	heta = \frac{9\pi}{4}$$, what is the reference angle?

Accepted Answer

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

Question 20

A Ferris wheel makes a full rotation every 360 seconds. If a seat starts at the lowest point, what is the coterminal angle after 750 seconds?

Accepted Answer

$$30^\circ$$

Trigonometric Functions of Any Angle: Definitions, Signs, Coterminal Angles, and Reference Angles

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