Q: Which of the following is a Pythagorean identity?

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

Q: Which trigonometric functions are odd?

$$\tan \theta, \sin \theta, \csc \theta$$

Question 1

Which of the following points lies on the unit circle?

Accepted Answer

$$(\frac{3}{5}, \frac{4}{5})$$

Question 2

Given $$\sin 	heta = \frac{3}{5}$$ and $$	heta is in $$the first quadrant, what is $$\cos 	heta$$?

Accepted Answer

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

Question 3

Evaluate $$\cos \left( \frac{5\pi}{6} \right).$$

Accepted Answer

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

Question 4

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

Accepted Answer

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

Question 5

Which of the following is a Pythagorean identity?

Accepted Answer

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

Question 6

Given $$\sin 	heta = \frac{5}{13}$$ and $$	heta is in $$quadrant II, what is $$\cos 	heta$$?

Accepted Answer

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

Question 7

Which trigonometric functions are odd?

Accepted Answer

$$	an 	heta, \sin 	heta, \csc 	heta$$

Question 8

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

Accepted Answer

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

Question 9

Evaluate $$\cot \left( \frac{5\pi}{6} \right).$$

Accepted Answer

$$-\sqrt{3}$$

Question 10

Which of the following is the correct expression for $$\sec^2$ 	heta in $$terms of $$	an 	heta$$?

Accepted Answer

$$1 + 	an^2$ 	heta$$

Question 11

A ladder leans against a wall making an angle $$	heta$$ with the ground. If the top of the ladder is 5 meters above the ground and the base is 2 meters from the wall, what is $$\sin 	heta$$?

Accepted Answer

$$\frac{5}{\sqrt{29}}$$

Question 12

Which of the following is true for the point $$(x, y) on $$the unit circle?

Accepted Answer

$$x^2$$ + $$y^2 = 1$

Question 13

If $$\sin 	heta = \frac{3}{5}$$ and $$	an 	heta = 0$$, what is $$	heta$$?

Accepted Answer

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

Question 14

Which of the following is an even trigonometric function?

Accepted Answer

$$\cos 	heta$$

Question 15

Evaluate $$\sin \left( \frac{2\pi}{3} \right).$$

Accepted Answer

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

Question 16

If $$\cos 	heta = -\frac{4}{5}$$ and $$	heta is in $$quadrant III, what is $$\sin 	heta$$?

Accepted Answer

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

Question 17

Which of the following is the correct expression for $$\csc^2$ 	heta in $$terms of $$\cot 	heta$$?

Accepted Answer

$$1 + \cot^2$ 	heta$$

Question 18

If $$\sin 	heta = \frac{5}{13}$$ and $$	heta is in $$quadrant II, what is $$	an 	heta$$?

Accepted Answer

$$-\frac{5}{12}$$

Question 19

Which of the following is the value of $$\cos \left( \frac{\pi}{3} \right)$$?

Accepted Answer

$$\frac{1}{2}$$

Question 20

If $$	an 	heta = \frac{5}{12}$$ and $$	heta is in $$quadrant III, what is $$\sin 	heta$$?

Accepted Answer

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

Trigonometric Functions and the Unit Circle: Key Concepts and Identities

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