Question 1

Convert the angle $$83^	ext{\circ}32'28'' to a $$decimal in degrees. Round your answer to two decimal places.

Accepted Answer

$$83.54^	ext{\circ}$$

Question 2

Convert $$149.57^	ext{\circ} to $$degrees, minutes, and seconds ($$D^	ext{\circ}M'S'') $$form. Round to the nearest second.

Accepted Answer

$$149^	ext{\circ}34'12''$$

Question 3

A circle has radius $$r = 12$$ feet and arc length $$s = 12$$ feet. What is the central angle $$	heta in $$radians?

Accepted Answer

$$1$$	ext{ radian}$

Question 4

Convert $$87^	ext{\circ} to $$radians. Express your answer as a multiple of $$\pi.$$

Accepted Answer

$$\dfrac{29\pi}{60}$$

Question 5

Convert $$\dfrac{11\pi}{10}$$ radians to degrees.

Accepted Answer

$$198^	ext{\circ}$$

Question 6

Find the area of a sector of a circle with radius $$12$$ inches and central angle $$90^	ext{\circ}. $$Round your answer to two decimal places.

Accepted Answer

$$113.04$$	ext{ in}^2$

Question 7

An object travels around a circle of radius $$20$$ meters. In $$10$$ seconds, it sweeps out a central angle of $$\dfrac{1}{5}$$ radian. What is its linear speed?

Accepted Answer

$$\dfrac{2}{5}$$	ext{ m/sec}$

Question 8

Find the exact value of $$	an 45^	ext{\circ} - \sin 60^	ext{\circ}.$$

Accepted Answer

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

Question 9

If $$\sin 	heta \u003e 0$$ and $$\cos 	heta \u003c 0$$, in which quadrant does $$	heta$$ lie?

Accepted Answer

Quadrant II

Question 10

If $$\csc 	heta \u003e 0$$ and $$\sec 	heta \u003e 0$$, in which quadrant does $$	heta$$ lie?

Accepted Answer

Quadrant I

Question 11

A point $$(3, -2)$$ lies on the terminal side of angle $$	heta. $$Find $$	an 	heta.$$

Accepted Answer

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

Question 12

If $$	an 	heta = -\dfrac{24}{7}$$ and $$90^	ext{\circ} \u003c 	heta \u003c 180^	ext{\circ}$$, find $$\cos 	heta.$$

Accepted Answer

$$-\dfrac{7}{25}$$

Question 13

Use the even-odd properties to find the exact value of $$\cos\left(-\dfrac{\pi}{4}\right).$$

Accepted Answer

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

Question 14

A surveyor is measuring the distance across a lake. He sets up his transit $$120$$ feet from a piling directly across from a pier. The angle between the piling and the pier is $$30^	ext{\circ}. $$What is the distance between the piling and the pier, to the nearest foot?

Accepted Answer

$$69$$	ext{ ft}$

Question 15

From the edge of a $$1000-$$foot cliff, the angles of depression to two cars in the valley below are $$21^	ext{\circ}$$ and $$28^	ext{\circ}. $$How far apart are the cars? Round your answer to the nearest $$0.1 ft.$$

Accepted Answer

$$724.4$$	ext{ ft}$

Question 16

Find the exact value of $$\sec^2$ 20^	ext{\circ} - 	an^2$ 20^	ext{\circ}.$$

Accepted Answer

$$1$$

Question 17

If $$\csc 	heta = -\dfrac{3}{2}$$ and $$	heta is in $$quadrant III, find $$\cot 	heta.$$

Accepted Answer

$$\dfrac{5}{2}$$

Question 18

Use the periodicity of trigonometric functions to find the exact value of $$\sin 765^	ext{\circ}.$$

Accepted Answer

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

Question 19

Use the periodicity of trigonometric functions to find the exact value of $$	an 750^	ext{\circ}.$$

Accepted Answer

$$\dfrac{\sqrt{3}}{3}$$

Question 20

The blade of a windshield wiper sweeps out an angle of $$135^	ext{\circ} in $$one cycle. The base of the blade is $$12$$ inches from the pivot point and the tip is $$32$$ inches from the pivot point. What area does the wiper cover in one cycle? (Round to the nearest $$0.1$$ square inch.)

Accepted Answer

$$1036.7$$	ext{ in}^2$

Precalculus Exam 1 Review: Step-by-Step Guidance

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