Question 1

A point $$(-12, 5)$$ lies on the terminal side of an angle $$	heta in $$standard position. What is $$\sin 	heta$$?

Accepted Answer

$$\dfrac{5}{13}$$

Question 2

Given $$	an 	heta = \dfrac{4}{3}$$ and $$\cos 	heta \u003c 0$$, which quadrant does $$	heta$$ lie in?

Accepted Answer

Quadrant II

Question 3

Evaluate $$\sec \left( \dfrac{\pi}{2} \right).$$

Accepted Answer

Undefined

Question 4

Find the reference angle for $$240^\circ.$$

Accepted Answer

$$60^\circ$$

Question 5

Find the reference angle for $$\dfrac{11\pi}{3}.$$

Accepted Answer

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

Question 6

If $$	an 	heta = -1$$, which quadrant could $$	heta be in$$?

Accepted Answer

Quadrant II or IV

Question 7

Evaluate $$\cot \left( \dfrac{3\pi}{2} \right).$$

Accepted Answer

Undefined

Question 8

Use reference angles to find the exact value: $$\csc(-210^\circ).$$

Accepted Answer

$$-2$$

Question 9

Find the exact value: $$\sin \dfrac{\pi}{3} \cos \dfrac{\pi}{4} - \cos \dfrac{\pi}{3} \sin \dfrac{\pi}{4}.$$

Accepted Answer

$$\dfrac{\sqrt{2}}{2}$$

Question 10

Find the exact value: $$\cos \dfrac{\pi}{6} \cos \dfrac{\pi}{3} - \sin \dfrac{\pi}{6} \sin \dfrac{\pi}{3}.$$

Accepted Answer

$$\dfrac{1}{2}$$

Question 11

Evaluate $$1 + \cot \left( \dfrac{\pi}{4} \right).$$

Accepted Answer

2

Question 12

Evaluate $$\csc \left( \dfrac{5\pi}{4} \right).$$

Accepted Answer

$$-\sqrt{2}$$

Question 13

Given $$\sec 	heta \u003e 0$$ and $$	an 	heta \u003c 0$$, in which quadrant does $$	heta$$ lie?

Accepted Answer

Quadrant IV

Question 14

Given $$\csc 	heta  0$$, in which quadrant does $$	heta$$ lie?

Accepted Answer

Quadrant III

Question 15

If $$	heta is an $$angle in standard position and $$\cos 	heta = -\dfrac{12}{13}$$, what is $$\sec 	heta$$?

Accepted Answer

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

Question 16

If $$	an 	heta = \dfrac{4}{3}$$ and $$\cos 	heta \u003c 0$$, what is $$\sin 	heta$$?

Accepted Answer

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

Question 17

Find the reference angle for $$-\dfrac{17\pi}{4}.$$

Accepted Answer

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

Question 18

Find the reference angle for $$\dfrac{23\pi}{6}.$$

Accepted Answer

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

Question 19

Evaluate $$\cot \left( \dfrac{\pi}{3} \right).$$

Accepted Answer

$$\dfrac{1}{\sqrt{3}}$$

Trigonometric Functions, Reference Angles, and Quadrant Analysis

Study Guide - Practice Questions