Question 1

Given the point $(-5, 12)$ lies on the terminal side of angle $	heta$ in standard position, what is $\sin 	heta$?

Accepted Answer

$\dfrac{12}{13}$

Question 2

If $\cos 	heta = -\dfrac{3}{5}$ and $	heta$ is in Quadrant III, what is $	an 	heta$?

Accepted Answer

$\dfrac{4}{3}$

Question 3

A circle has radius $r = 5$ cm and a central angle $	heta = 72^\circ$. What is the exact arc length $s$ cut off by $	heta$?

Accepted Answer

$2\pi$ cm

Question 4

Simplify the expression $	an 25^\circ \cdot \cot 25^\circ + \sin^2 40^\circ + \cos^2 40^\circ + \sin \dfrac{\pi}{2}$.

Accepted Answer

$2$

Question 5

Evaluate exactly: $\sin(-30^\circ) + \cos(-60^\circ) + 	an(-45^\circ)$.

Accepted Answer

$-1$

Question 6

For $f(x) = -4 \sin \left(\dfrac{1}{3}x\right)$, what is the period?

Accepted Answer

$6\pi$

Question 7

Which of the following is the correct value for $\cos\left(x - 2\pi\right) + 3\cos\left(x + 4\pi\right) - \cos\left(x + 6\pi\right)$ if $\cos x = 0.7$?

Accepted Answer

$-2.1$

Question 8

Using an isosceles right triangle, what is $\sin 45^\circ$?

Accepted Answer

$\dfrac{\sqrt{2}}{2}$

Question 9

Find the reference angle for $	an(-120^\circ)$ and evaluate it exactly.

Accepted Answer

$\sqrt{3}$

Question 10

Simplify using cofunction identities: $\dfrac{\sin 25^\circ}{\cos 65^\circ} + \dfrac{\cos 40^\circ}{\sin 50^\circ}$.

Accepted Answer

$2$

Question 11

If $\cos x = 0.7$, what is $\cos(x + 4\pi)$?

Accepted Answer

$0.7$

Question 12

For $g(x) = 3 \cos(-2x)$, what is the amplitude?

Accepted Answer

$3$

Question 13

What is the exact value of $\cot 30^\circ + \dfrac{\sin 30^\circ}{\cos 60^\circ - 	an 45^\circ}$?

Accepted Answer

$\sqrt{3}$

Question 14

Find the reference angle for $\cos \dfrac{5\pi}{4}$ and evaluate it exactly.

Accepted Answer

$-\dfrac{\sqrt{2}}{2}$

Question 15

If $\cos 	heta = -\dfrac{3}{5}$ and $	heta$ is in Quadrant III, what is $\sin 	heta$?

Accepted Answer

$-\dfrac{4}{5}$

Question 16

What is the amplitude of $f(x) = -4 \sin \left(\dfrac{1}{3}x\right)$?

Accepted Answer

$4$

Question 17

What is the area of a sector with radius $5$ cm and central angle $72^\circ$?

Accepted Answer

$5\pi$ cm$^2$

Question 18

What is the exact value of $\sin 210^\circ$?

Accepted Answer

$-\dfrac{1}{2}$

Question 19

If $	an 25^\circ = x$, what is $	an 25^\circ \cdot \cot 25^\circ$?

Accepted Answer

$1$

Question 20

Which of the following is the period of $g(x) = 3 \cos(-2x)$?

Accepted Answer

$\pi$

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