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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