$$\sin \theta = \dfrac{-3}{\sqrt{10}}$$

$$\theta' = 210^\circ - 180^\circ = 30^\circ$$

$$\sin \theta = -\dfrac{1}{\sqrt{10}}$$

$$\cos \theta = \dfrac{1}{17}$$

Question 1

Let $$P = (1, -3) be a $$point on the terminal side of angle $$	heta. $$What is the value of $$r$$?

Accepted Answer

$$r = \sqrt{1^2$ + (-3)^2$} = \sqrt{10}$$

Question 2

Given $$P = (1, -3) on $$the terminal side of $$	heta$$, what is $$\sin 	heta$$?

Accepted Answer

$$\sin 	heta = \dfrac{-3}{\sqrt{10}}$$

Question 3

Which trigonometric functions are positive in Quadrant II?

Accepted Answer

Sine and cosecant

Question 4

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

Accepted Answer

Quadrant IV

Question 5

Evaluate $$\cos 0^\circ$$ and $$\csc 0^\circ.$$

Accepted Answer

$$\cos 0^\circ = 1$$, $$\csc 0^\circ is $$undefined

Question 6

Find the reference angle for $$	heta = 210^\circ.$$

Accepted Answer

$$	heta' = 210^\circ - 180^\circ = 30^\circ$$

Question 7

Given $$	an 	heta = -\dfrac{1}{3}$$ and $$\cos 	heta \u003c 0$$, what is $$\sin 	heta$$?

Accepted Answer

$$\sin 	heta = -\dfrac{1}{\sqrt{10}}$$

Question 8

What is the reference angle for $$	heta = -240^\circ$$?

Accepted Answer

$$	heta' = 60^\circ$$

Question 9

Use reference angles to find the exact value of $$\sin 300^\circ.$$

Accepted Answer

$$\sin 300^\circ = -\dfrac{1}{2}$$

Question 10

If $$\sec 	heta = 17$$ and $$	an 	heta \u003e 0$$, what is $$\cos 	heta$$?

Accepted Answer

$$\cos 	heta = \dfrac{1}{17}$$

Question 11

Which of the following is the correct definition of the reference angle?

Accepted Answer

The acute angle between the terminal side of an angle and the x-axis

Question 12

Find the reference angle for $$	heta = 665^\circ.$$

Accepted Answer

$$	heta' = 85^\circ$$

Question 13

Evaluate $$\cos \dfrac{\pi}{2}$$ and $$\csc \dfrac{\pi}{2}.$$

Accepted Answer

$$\cos \dfrac{\pi}{2} = 0$$, $$\csc \dfrac{\pi}{2} = 1$$

Question 14

If $$	an 	heta  0$$, in which quadrant does $$	heta$$ lie?

Accepted Answer

Quadrant IV

Question 15

Use reference angles to find the exact value of $$	an \dfrac{5\pi}{4}.$$

Accepted Answer

$$	an \dfrac{5\pi}{4} = 1$$

Question 16

What is the reference angle for $$	heta = -\dfrac{11\pi}{3}$$?

Accepted Answer

$$	heta' = \dfrac{\pi}{3}$$

Question 17

Evaluate $$\cos 180^\circ$$ and $$\csc 180^\circ.$$

Accepted Answer

$$\cos 180^\circ = -1$$, $$\csc 180^\circ is $$undefined

Question 18

If $$\sin 	heta \u003e 0$$ and $$	an 	heta \u003e 0$$, in which quadrant does $$	heta$$ lie?

Accepted Answer

Quadrant I

Question 19

Use reference angles to find the exact value of $$\sec\left(-\dfrac{\pi}{6}\right).$$

Accepted Answer

$$\sec\left(-\dfrac{\pi}{6}\right) = \dfrac{2}{\sqrt{3}}$$

Trigonometric Functions of Any Angle and Reference Angles

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