$$\csc \theta$$ and $$\cot \theta$$

$$\tan \theta$$ and $$\cot \theta$$

$$\alpha = \theta - 180^\circ$$

Question 1

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

Accepted Answer

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

Question 2

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

Accepted Answer

$$60^\circ$$

Question 3

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

Accepted Answer

Quadrant IV

Question 4

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

Accepted Answer

$$45^\circ$$

Question 5

What is the exact value of $$\cos 135^\circ$$?

Accepted Answer

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

Question 6

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

Accepted Answer

Positive

Question 7

Which trigonometric functions are always positive in Quadrant I?

Accepted Answer

All six trigonometric functions

Question 8

Find the exact value of $$\cos 390^\circ.$$

Accepted Answer

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

Question 9

Given $$	an 	heta = -3$$ and $$\cos 	heta \u003c 0$$, what is the exact value of $$\sec 	heta$$?

Accepted Answer

$$-\frac{\sqrt{10}}{1}$$

Question 10

If $$	heta = 0^\circ$$, which trigonometric functions are not defined?

Accepted Answer

$$\csc 	heta$$ and $$\cot 	heta$$

Question 11

A Ferris wheel rotates through an angle of $$600^\circ. $$What is the reference angle for this rotation?

Accepted Answer

$$60^\circ$$

Question 12

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

Accepted Answer

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

Question 13

Which of the following is a correct definition for $$	an 	heta in $$terms of coordinates $$(a, b)$$ and $$r$$?

Accepted Answer

$$	an 	heta = \frac{b}{a}$$

Question 14

If an angle $$	heta$$ has a terminal side passing through the point $$(-1, 3)$$, what is the value of $$r$$?

Accepted Answer

$$\sqrt{10}$$

Question 15

Which of the following best describes coterminal angles?

Accepted Answer

Angles with the same terminal side

Question 16

If $$	heta is in $$Quadrant III, which trigonometric functions are positive?

Accepted Answer

$$	an 	heta$$ and $$\cot 	heta$$

Question 17

A ramp is built at an angle of $$150^\circ$$ from the positive x-axis. What is the reference angle for this ramp?

Accepted Answer

$$30^\circ$$

Question 18

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

Accepted Answer

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

Question 19

Which of the following is the correct formula for the reference angle $$\alpha$$ for an angle $$	heta in $$Quadrant III?

Accepted Answer

$$\alpha = 	heta - 180^\circ$$

Trigonometric Functions of Any Angle: Definitions, Properties, and Applications

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