Question 1

A circular racetrack has a radius of $$12$$ meters. If a runner completes an arc length of $$18$$ meters, what is the central angle in radians subtended by this arc?

Accepted Answer

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

Question 2

A sector of a circle has an area of $$20$$ square meters and a central angle of $$4$$ radians. What is the radius of the circle? (Round to two decimal places)

Accepted Answer

$$2.24$$

Question 3

Convert $$120^	ext{o} to $$radians.

Accepted Answer

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

Question 4

Convert $$-\frac{9\pi}{4}$$ radians to degrees.

Accepted Answer

$$-405^	ext{o}$$

Question 5

Given $$\csc(	heta) = -\frac{7}{8}$$ and $$	heta is $$acute, what is $$\sin(	heta)$$?

Accepted Answer

Question 6

The point $$(-4,7)$$ lies on the terminal side of angle $$	heta in $$standard position. What is $$\sin(	heta)$$?

Accepted Answer

$$\frac{7}{\sqrt{65}}$$

Question 7

Find the exact value of $$	an\left(\frac{13\pi}{6}ight).$$

Accepted Answer

$$\frac{1}{\sqrt{3}}$$

Question 8

Find the exact value of $$\sec\left(-\frac{17\pi}{4}\right).$$

Accepted Answer

$$\sqrt{2}$$

Question 9

Given $$\cot(	heta) = \frac{2}{5}$$ and $$\cos(	heta) \u003e 0$$, what is $$\csc(	heta)$$?

Accepted Answer

$$\frac{\sqrt{29}}{5}$$

Question 10

A Ferris wheel rotates such that the height of a passenger above the ground can be modeled by $$h(x) = 5\cos(x) - 8. $$What is the amplitude of the motion?

Accepted Answer

$$5$$

Question 11

For the function $$g(x) = -\sin\left(\frac{\pi}{3}x\right)$$, what is the period?

Accepted Answer

$$6$$

Question 12

For the function $$h(x) = \cos\left(x + \frac{\pi}{6}\right)$$, what is the phase shift?

Accepted Answer

$$-\frac{\pi}{6}$$

Question 13

For the function $$j(x) = 5\sec(x) - 8$$, what is the vertical shift?

Accepted Answer

$$-8$$

Question 14

For the function $$k(x) = -\csc\left(\frac{\pi}{3}x\right)$$, what is the amplitude?

Accepted Answer

The amplitude is not defined for $$\csc$$ functions.

Question 15

A pizza with a radius of $$10$$ inches is sliced into a sector with a central angle of $$60^	ext{o}. $$What is the area of the sector? (Round to two decimal places)

Accepted Answer

$$52.36$$

Question 16

A clock's minute hand is $$15 cm $$long. How far does the tip of the minute hand travel in $$20$$ minutes?

Accepted Answer

$$31.42 cm$$

Question 17

A satellite orbits Earth in a circular path with radius $$7000 km. If it $$sweeps out a central angle of $$0.5$$ radians, what is the arc length it travels?

Accepted Answer

$$3500 km$$

Question 18

If $$\sin(	heta) = \frac{3}{5}$$ and $$	heta is in $$Quadrant II, what is $$\cos(	heta)$$?

Accepted Answer

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

Question 19

A pendulum swings through an angle of $$\frac{\pi}{4}$$ radians. If the length of the pendulum is $$2$$ meters, what is the arc length traced by the pendulum?

Accepted Answer

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

Question 20

A sector of a circle has a radius of $$6$$ meters and a central angle of $$120^	ext{o}. $$What is the area of the sector? (Round to two decimal places)

Accepted Answer

$$37.70$$

Precalculus Test 1 Review – Step-by-Step Study Guidance

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