Q: Which of the following is the correct trigonometric form of $$1 + \\sqrt{3}i$$?

$$2(\\cos(\\frac{\\pi}{3}) + i\\sin(\\frac{\\pi}{3}))$$

Q: Which of the following is the correct polar form for the point $$(-2, 3)$$?

$$(\\sqrt{13}, \\arctan(-1.5) + \\pi)$$

Question 1

Convert $$47^\circ 29' to $$decimal degrees. Round your answer to the nearest thousandth.

Accepted Answer

$$47.483^\circ$$

Question 2

A plane flies 4 hours at 100 mph on a bearing of $$40^\circ$$, then turns and flies for 3 hours at the same speed on a bearing of $$130^\circ. $$How far is the plane from the starting point?

Accepted Answer

$$609$$ miles

Question 3

Evaluate $$\sin(540^\circ) ($$write the exact answer).

Accepted Answer

$$0$$

Question 4

Given $$\cos\theta = \frac{2}{5}$$ and $$\theta is in $$the fourth quadrant, find $$\sin\theta.$$

Accepted Answer

$$-\frac{\sqrt{21}}{5}$$

Question 5

Which of the following is the correct period for the function $$y = 3\tan(2x)$$?

Accepted Answer

$$\frac{\pi}{2}$$

Question 6

The Earth rotates on its axis once every 24 hours. If the Earth's radius is $$6400 km$$, what is the linear speed at the equator? (Round to the nearest hundred km/hr)

Accepted Answer

$$1700 km/hr$$

Question 7

Find the exact value of $$\tan(\arccos(\frac{1}{3})).$$

Accepted Answer

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

Question 8

Which of the following is the correct trigonometric form of $$1 + \sqrt{3}i$$?

Accepted Answer

$$2(\cos(\frac{\pi}{3}) + i\sin(\frac{\pi}{3}))$$

Question 9

A Ferris wheel has a radius of $$75 ft. If a $$person takes a seat and the wheel turns $$\frac{\pi}{2}$$ radians, how far has the person traveled?

Accepted Answer

$$37.5\pi ft$$

Question 10

Which of the following is the correct value for $$\sin(1020^\circ)$$?

Accepted Answer

$$-\frac{1}{2}$$

Question 11

Given $$\sin\alpha = \frac{3}{5}$$ and $$\alpha is in $$quadrant II, what is $$\cos\alpha$$?

Accepted Answer

$$-\frac{4}{5}$$

Question 12

Which of the following is the correct amplitude for the function $$y = 2\sin x$$?

Accepted Answer

$$2$$

Question 13

If $$\tan\theta = 2$$ and $$\theta is in $$the second quadrant, what is $$\sin\theta$$?

Accepted Answer

$$-\frac{2}{\sqrt{5}}$$

Question 14

Which of the following is the correct rectangular form of $$2(\cos 270^\circ + i \sin 270^\circ)$$?

Accepted Answer

$$0 - 2i$$

Question 15

A ship sails $$18.5 km on a $$bearing of $$180^\circ$$, then turns and sails $$4.7 km on a $$bearing of $$317^\circ. $$What is the distance from the starting point to the ship's final position? (Round to the nearest tenth of a kilometer)

Accepted Answer

$$23.0 km$$

Question 16

Which of the following is the correct value for $$\arccos(-\frac{1}{2}) in $$radians?

Accepted Answer

$$\frac{2\pi}{3}$$

Question 17

Which of the following is the correct polar form for the point $$(-2, 3)$$?

Accepted Answer

$$(\sqrt{13}, \arctan(-1.5) + \pi)$$

Question 18

Which of the following is the correct value for $$\sec(\frac{\pi}{2})$$?

Accepted Answer

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Question 19

Which of the following is the correct value for $$\arcsin(1) in $$radians?

Accepted Answer

$$\frac{\pi}{2}$$

Comprehensive Trigonometry Final Exam Review – Study Guide

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