$\cos \theta = \frac{\sqrt{21}}{11}$

Question 1

Given the point $P(\sqrt{7}, -3)$ on the terminal side of angle $	heta$ in standard position (see image a), find $\sin 	heta$.

Accepted Answer

$\sin 	heta = \frac{-3}{4}$

Question 2

Given the point $(-2, 11)$ on the terminal side of angle $\beta$ in standard position (see image b), what is $\cos \beta$?

Accepted Answer

$\cos \beta = \frac{-2}{\sqrt{125}}$

Question 3

For the point $(9, 1)$ on the terminal side of angle $\alpha$ (see image c), what is $	an \alpha$?

Accepted Answer

$	an \alpha = \frac{1}{9}$

Question 4

Which of the following is the correct value for $\sin 30^\circ$?

Accepted Answer

$\frac{1}{2}$

Question 5

Convert $-135^\circ$ to radians in terms of $\pi$.

Accepted Answer

$-\frac{3\pi}{4}$

Question 6

If $\sin 	heta = \frac{10}{11}$ and $	heta$ is in Quadrant I, what is $\cos 	heta$?

Accepted Answer

$\cos 	heta = \frac{\sqrt{21}}{11}$

Question 7

Find the amplitude and period of the function $y = 2 \cos \left( \frac{1}{2}x - \frac{\pi}{2} \right)$.

Accepted Answer

Amplitude: $2$, Period: $4\pi$

Question 8

An arc 18 m long on a circle of radius 8 m subtends an angle of how many radians?

Accepted Answer

$\frac{9}{4}$ radians

Question 9

If $	an \beta = 5$ and $\beta$ is in Quadrant I, what is $\sin \beta$?

Question 10

What is the reference angle for $-45^\circ$?

Accepted Answer

$45^\circ$

Question 11

Given $\cos \alpha = -\frac{4}{5}$ and $\alpha$ is in Quadrant II, what is $\sin \alpha$?

Accepted Answer

$\frac{3}{5}$

Question 12

Find the length of an arc of a circle of radius 5 cm associated with an angle of $\frac{2\pi}{3}$ radians.

Accepted Answer

$\frac{10\pi}{3}$ cm

Question 13

What is the period of the function $y = 4 \sin \left( \frac{1}{4}x + \frac{\pi}{8} \right)$?

Accepted Answer

$8\pi$

Question 14

Which of the following is the correct value for $	an 60^\circ$?

Accepted Answer

$\sqrt{3}$

Question 15

Convert $\frac{7\pi}{6}$ radians to degrees.

Accepted Answer

$210^\circ$

Question 16

If $\sin 	heta = \frac{2\sqrt{2}}{3}$, $\cos 	heta = \frac{1}{3}$, and $	an 	heta = 2\sqrt{2}$, what is $\sec 	heta$?

Accepted Answer

$3$

Question 17

What is the amplitude of the function $y = -\sin(x + \frac{\pi}{2})$?

Accepted Answer

$1$

Question 18

What is the value of $	an 270^\circ$?

Accepted Answer

Undefined

Question 19

Which transformation describes the graph of $y = \sin x + 1$ compared to $y = \sin x$?

Accepted Answer

A vertical shift upward by 1 unit

Question 20

What is the value of $\sin 300^\circ$?

Accepted Answer

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

Finding Trigonometric Function Values from a Point on the Coordinate Plane

Study Guide - Practice Questions