Q: Which of the following is the correct reciprocal identity for $\tan \theta$?

$\tan \theta = \dfrac{1}{\cot \theta}$

Q: Which trigonometric functions are positive in Quadrant III?

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

Q: Determine if $\sin \theta = 2.5$ is possible for any real $\theta$.

Impossible, because $-1 \leq \sin \theta \leq 1$

Q: Given $\tan \theta = 110.47$, is this value possible for some $\theta$?

Yes, because $\tan \theta$ can take any real value

Q: If $\sec \theta = 0.6$, is this value possible for any real $\theta$?

No, because $|\sec \theta| \geq 1$

Q: Which of the following is a Pythagorean identity?

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

Q: Which quotient identity correctly expresses $\tan \theta$ in terms of $\sin \theta$ and $\cos \theta$?

$\tan \theta = \dfrac{\sin \theta}{\cos \theta}$

Q: A surveyor measures an angle of $300^\circ$ from the positive $x$-axis. Which trigonometric functions are positive for this angle?

$\cos \theta$ and $\sec \theta$

Q: Which of the following statements about the range of $\tan \theta$ is correct?

$\tan \theta$ can take any real value

Q: A pilot is flying in Quadrant IV. Which trigonometric functions are positive for the angle of elevation?

$\cos \theta$ and $\sec \theta$

Question 1

Which of the following is the correct reciprocal identity for $	an 	heta$?

Accepted Answer

$	an 	heta = \dfrac{1}{\cot 	heta}$

Question 2

Given $\sec 	heta = \dfrac{5}{3}$, what is $\cos 	heta$?

Accepted Answer

$\dfrac{3}{5}$

Question 3

If $\csc 	heta = -\dfrac{\sqrt{12}}{2}$, what is $\sin 	heta$?

Accepted Answer

$-\dfrac{\sqrt{3}}{3}$

Question 4

In which quadrant is $\sin 	heta > 0$ and $	an 	heta < 0$?

Accepted Answer

Quadrant II

Question 5

Which trigonometric functions are positive in Quadrant III?

Accepted Answer

$	an 	heta$ and $\cot 	heta$

Question 6

Determine if $\sin 	heta = 2.5$ is possible for any real $	heta$.

Accepted Answer

Impossible, because $-1 \leq \sin 	heta \leq 1$

Question 7

Given $	an 	heta = 110.47$, is this value possible for some $	heta$?

Accepted Answer

Yes, because $	an 	heta$ can take any real value

Question 8

If $\sec 	heta = 0.6$, is this value possible for any real $	heta$?

Accepted Answer

No, because $|\sec 	heta| \geq 1$

Question 9

Suppose $\sin 	heta = \dfrac{2}{3}$ and $	heta$ is in Quadrant II. What is $\cos 	heta$?

Accepted Answer

$-\dfrac{\sqrt{5}}{3}$

Question 10

Given $	an 	heta = -2$ and $	heta$ is in Quadrant III, what is the sign of $\sin 	heta$ and $\cos 	heta$?

Accepted Answer

Both are negative

Question 11

Which of the following is a Pythagorean identity?

Accepted Answer

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

Question 12

If $\cos 	heta = -\dfrac{2}{5}$ and $	heta$ is in Quadrant III, what is $\sin 	heta$?

Accepted Answer

$-\dfrac{\sqrt{21}}{5}$

Question 13

Which quotient identity correctly expresses $	an 	heta$ in terms of $\sin 	heta$ and $\cos 	heta$?

Accepted Answer

$	an 	heta = \dfrac{\sin 	heta}{\cos 	heta}$

Question 14

A surveyor measures an angle of $300^\circ$ from the positive $x$-axis. Which trigonometric functions are positive for this angle?

Accepted Answer

$\cos 	heta$ and $\sec 	heta$

Question 15

If $\sin 	heta = \dfrac{4}{5}$ and $	heta$ is in Quadrant II, what is $	an 	heta$?

Accepted Answer

$-\dfrac{4}{3}$

Question 16

Which of the following statements about the range of $	an 	heta$ is correct?

Accepted Answer

$	an 	heta$ can take any real value

Question 17

Given $\cos 	heta = a$ and $a > 0$, what is $\sin 	heta$ using the Pythagorean identity?

Accepted Answer

$\sin 	heta = \sqrt{1 - a^2}$

Question 18

A pilot is flying in Quadrant IV. Which trigonometric functions are positive for the angle of elevation?

Accepted Answer

$\cos 	heta$ and $\sec 	heta$

Question 19

If $\cot 	heta = 0$, what is $	an 	heta$?

Accepted Answer

$	an 	heta$ is undefined

Trigonometric Functions: Definitions, Identities, and Signs

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