Q: Which of the following is the correct cofunction identity for $\\sin(\\theta)$?

$\\sin(\\theta) = \\cos(90^\\circ - \\theta)$

Q: If $\\tan(\\theta) = -1$ and $0 < \\theta < 2\\pi$, what are the possible values for $\\theta$?

$\\frac{3\\pi}{4}, \\frac{7\\pi}{4}$

Q: Which of the following is the reciprocal identity for $\\sec(\\theta)$?

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

Q: If $\\sin(\\theta) = -\\frac{\\sqrt{2}}{2}$ and $0 < \\theta < 2\\pi$, what are the possible values for $\\theta$?

$\\frac{5\\pi}{4}, \\frac{7\\pi}{4}$

Question 1

Which of the following best describes a coterminal angle to $370^\circ$?

Accepted Answer

$10^\circ$

Question 2

A right triangle has legs of length 5 and 5. What is the length of the hypotenuse?

Accepted Answer

$5\sqrt{2}$

Question 3

Convert $540^\circ$ to radians.

Accepted Answer

$3\pi$

Question 4

Which of the following is the reference angle for $210^\circ$?

Accepted Answer

$30^\circ$

Question 5

If $\sin(\theta) = \frac{3}{5}$ and $\theta$ is in Quadrant II, what is $\cos(\theta)$?

Accepted Answer

$-\frac{4}{5}$

Question 6

A hiking path rises 500 feet over a horizontal distance of 4000 feet. What is the angle of inclination of the path? (Round to the nearest degree.)

Accepted Answer

$7^\circ$

Question 7

Which of the following is the correct value for $\tan(45^\circ)$?

Accepted Answer

$1$

Question 8

Given $\cos(\theta) = -\frac{1}{2}$ and $0 < \theta < 2\pi$, which quadrant(s) could $\theta$ be in?

Accepted Answer

Quadrant II and III

Question 9

What is the sine of $30^\circ$?

Accepted Answer

$\frac{1}{2}$

Question 10

A right triangle has an angle of $31^\circ$ and a hypotenuse of 8.0. What is the length of the side adjacent to the $31^\circ$ angle? (Round to 3 decimal places.)

Accepted Answer

$6.857$

Question 11

Which of the following is the correct cofunction identity for $\sin(\theta)$?

Accepted Answer

$\sin(\theta) = \cos(90^\circ - \theta)$

Question 12

If $\tan(\theta) = -1$ and $0 < \theta < 2\pi$, what are the possible values for $\theta$?

Accepted Answer

$\frac{3\pi}{4}, \frac{7\pi}{4}$

Question 13

Which of the following is the correct value for $\cos(60^\circ)$?

Accepted Answer

$\frac{1}{2}$

Question 14

A sailboat is observed from a lighthouse 240 ft tall, 2.2 km inland from the shore. If the angle of elevation to the top of the lighthouse from the boat is $3.4^\circ$, how far is the boat from the coastline? (Round to two decimal places.)

Accepted Answer

$3.89$ km

Question 15

Which of the following is the reciprocal identity for $\sec(\theta)$?

Accepted Answer

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

Question 16

Convert $\frac{5\pi}{6}$ radians to degrees.

Accepted Answer

$150^\circ$

Question 17

If $\sin(\theta) = -\frac{\sqrt{2}}{2}$ and $0 < \theta < 2\pi$, what are the possible values for $\theta$?

Accepted Answer

$\frac{5\pi}{4}, \frac{7\pi}{4}$

Question 18

Which of the following is NOT a possible positive angle in standard position?

Accepted Answer

$-54^\circ$

Question 19

Given $\tan(\theta) = \frac{1}{\sqrt{3}}$, what is $\theta$ in degrees in the interval $[0^\circ, 90^\circ]$?

Accepted Answer

$30^\circ$

Angles and the Trigonometric Functions: Comprehensive Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards