Question 1

Given the right triangle shown, if $$a = 48$$ and $$c = 50$$, what is $$	an B$$?

Accepted Answer

$$\dfrac{7}{24}$$

Question 2

Convert $$288^\circ to $$radians. Leave your answer as a multiple of $$\pi.$$

Accepted Answer

$$\dfrac{8\pi}{5}$$

Question 3

Find the exact value of $$\cos\left(-\dfrac{2\pi}{3}\right).$$

Accepted Answer

$$-\dfrac{1}{2}$$

Question 4

A fishing boat leaves port on a bearing of $$30^\circ$$ and travels $$13.4 mi. $$The boat then turns due east and travels $$4.0 mi. $$How far is the fishing boat from port?

Accepted Answer

$$15.8 mi$$

Question 5

Find the amplitude of $$y = -4 \sin(2x + \pi).$$

Accepted Answer

$$4$$

Question 6

If $$	an 	heta = \dfrac{12}{5}$$ and $$\pi \u003c 	heta \u003c \dfrac{3\pi}{2}$$, find $$\sin(2	heta).$$

Accepted Answer

$$\dfrac{120}{169}$$

Question 7

Find the area of a sector of a circle with radius $$7.4 mi $$and central angle $$314^\circ. $$Express your answer to the nearest tenth.

Accepted Answer

$$150.1 mi$^2$$

Question 8

Given $$\cos s = -\dfrac{2}{2}$$ for $$s \in [0, 2\pi)$$, what are the solutions?

Accepted Answer

$$\dfrac{3\pi}{4}, \dfrac{5\pi}{4}$$

Question 9

Find the exact value of $$\sin\left(\dfrac{4\pi}{3}\right).$$

Accepted Answer

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

Question 10

If $$\sec 	heta = -2$$ and $$\sin 	heta \u003c 0$$, what is $$	an 	heta$$?

Accepted Answer

$$-1$$

Question 11

Find the phase shift of $$y = -2 \sin\left(x - \dfrac{\pi}{4}\right).$$

Accepted Answer

$$\dfrac{\pi}{4}$$ units$$\; to $$the right

Question 12

Given vectors $$\mathbf{u} = \langle -5, -5 \rangle$$ and $$\mathbf{v} = \langle -3, 8 \rangle$$, find $$\mathbf{v} - \mathbf{u}.$$

Accepted Answer

$$\langle 2, 13 \rangle$$

Question 13

Which of the following is the correct cofunction identity for $$\cos 33^\circ$$?

Accepted Answer

$$\sin 57^\circ$$

Question 14

If $$	an x (\csc x - \sin x) = \cos x$$, which trigonometric identity is being verified?

Accepted Answer

Fundamental identities

Question 15

Find the dot product of $$\langle 5, -13 \rangle$$ and $$\langle 15, 15 \rangle.$$

Accepted Answer

$$-120$$

Question 16

Find the period of $$y = 3 \cos\left(3x + \dfrac{\pi}{2}\right).$$

Accepted Answer

$$\dfrac{2\pi}{3}$$

Question 17

Given $$\cos s = -\dfrac{5}{13}$$ with $$s in $$quadrant II, and $$\sin t = \dfrac{8}{17}$$ with $$t in $$quadrant II, find $$	an(s + t).$$

Accepted Answer

$$\dfrac{220}{21}$$

Question 18

Find the exact value of $$\arcsin\left(-\dfrac{1}{2}\right).$$

Accepted Answer

$$-\dfrac{\pi}{6}$$

Question 19

A wire is wound around a drum of radius $$1.49$$ meters through an angle of $$275.3^\circ. $$How much wire is wound (to the nearest hundredth of a meter)?

Accepted Answer

$$7.16 m$$

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