Q: Which trigonometric functions are positive in Quadrant III?

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

Q: Which of the following is the correct Pythagorean identity?

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

Q: Which of the following is a reciprocal identity?

$\sec \theta = \frac{1}{\cos \theta}$

Question 1

Given the point $(-3, 4)$ in the coordinate plane, which quadrant does this point lie in?

Accepted Answer

Quadrant II

Question 2

Given the point $(0, -5)$ in the coordinate plane, where is this point located?

Accepted Answer

On the negative $y$-axis

Question 3

If $\sin 	heta = -\frac{2}{3}$ and $	heta$ is in the quadrant where sine is negative and cosine is positive, which quadrant is $	heta$ in?

Accepted Answer

Quadrant IV

Question 4

Which trigonometric functions are positive in Quadrant III?

Accepted Answer

$	an 	heta$ and $\cot 	heta$

Question 5

If $	an 	heta > 0$ and $\csc 	heta < 0$, in which quadrant(s) could $	heta$ be?

Accepted Answer

Quadrant III

Question 6

Given $\cos 	heta = -\frac{2}{\sqrt{20}}$, what is $\sec 	heta$?

Accepted Answer

$-\sqrt{5}$

Question 7

Which of the following is an impossible value for a trigonometric function?

Accepted Answer

$\cos 	heta = -1.7$

Question 8

If $\sin 	heta = -\frac{\sqrt{2}}{3}$ and $\cos 	heta > 0$, what is $	an 	heta$?

Question 9

Given $\cot 	heta = -\frac{7}{24}$ and $	heta$ is in Quadrant II, what is $\sin 	heta$?

Accepted Answer

$\frac{24}{25}$

Question 10

Which identity is represented by $	an 	heta = \frac{\sin 	heta}{\cos 	heta}$?

Accepted Answer

Quotient Identity

Question 11

If $\sin 	heta = -\frac{2}{3}$, what is $\csc 	heta$?

Accepted Answer

$-\frac{3}{2}$

Question 12

Which of the following is the correct Pythagorean identity?

Accepted Answer

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

Question 13

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

Accepted Answer

$\frac{4}{5}$

Question 14

If $	an 	heta = 1.8$, what is $\cot 	heta$?

Accepted Answer

$\frac{1}{1.8}$

Question 15

Which of the following is a reciprocal identity?

Accepted Answer

$\sec 	heta = \frac{1}{\cos 	heta}$

Question 16

A ladder leans against a wall making an angle $	heta$ with the ground. If $\sin 	heta = 0.6$ and the ladder is $10$ ft long, how high up the wall does the ladder reach?

Accepted Answer

$6$ ft

Question 17

If $\cos 	heta = 0$, what is $\sec 	heta$?

Accepted Answer

Undefined

Question 18

Which quadrant contains angles where $\sin 	heta$ is positive and $	an 	heta$ is negative?

Accepted Answer

Quadrant II

Question 19

If $	an 	heta = \frac{8}{5}$ and $	heta$ is in Quadrant III, what is $\sin 	heta$?

Accepted Answer

$-\frac{8}{\sqrt{89}}$

Trigonometric Function Identities and Their Properties

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