Question 1

Convert $$135^{\circ} to $$radians. Which of the following is correct?

Accepted Answer

$$\frac{3\pi}{4}$$

Question 2

A central angle of $$54^{\circ}$$ subtends an arc on a circle of radius $$25.60 cm. $$What is the length of the arc?

Accepted Answer

$$24.13 cm$$

Question 3

Which of the following is the radian measure for $$-210^{\circ}$$?

Accepted Answer

$$-\frac{7\pi}{6}$$

Question 4

Given a circle with radius $$r = 0.327 m $$and a central angle of $$132.6^{\circ}$$, what is the arc length?

Accepted Answer

$$0.757 m$$

Question 5

If a satellite orbits Earth at a distance of $$8200 km $$from the center and completes one orbit ($$2\pi$$ radians) in $$2.5$$ hours, what is its linear speed?

Accepted Answer

$$21,000 km/hr$$

Question 6

What is $$\cos(150$$^{\circ}$$)$$?

Accepted Answer

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

Question 7

A pulley makes $$120$$ revolutions per minute. What is its angular speed in radians per second?

Accepted Answer

$$4\pi$$

Question 8

On the unit circle, what are the coordinates corresponding to $$330^{\circ}$$?

Accepted Answer

$$\left(\frac{\sqrt{3}}{2}, -\frac{1}{2}\right)$$

Question 9

If $$	heta = -3\pi$$, what is $$\sin(	heta)$$?

Accepted Answer

$$0$$

Question 10

A gear with radius $$3.6 in. $$rotates through $$150^{\circ}. $$What is the arc length traced by a point on the edge?

Accepted Answer

$$3\pi in.$$

Question 11

What is the value of $$	an\left(-\frac{9\pi}{4}ight)$$?

Accepted Answer

$$-1$$

Question 12

If a point moves at a linear speed of $$20\pi in/sec on a $$circle of radius $$5 in$$, what is its angular speed?

Accepted Answer

$$4\pi$$ 	ext{ radians/sec}$

Question 13

Which of the following is the reference angle for $$330^{\circ}$$?

Accepted Answer

$$30^{\circ}$$

Question 14

If $$\sin(s) = -\frac{\sqrt{3}}{2}$$ and $$s is in $$the fourth quadrant, what is $$s$$?

Accepted Answer

$$\frac{5\pi}{3}$$

Question 15

A circle has a radius of $$15 in. $$and rotates at $$\frac{\pi}{12}$$ radians per second. What is the linear speed of a point on the circumference?

Accepted Answer

$$\frac{5\pi}{4} in/sec$$

Question 16

What is the value of $$\sec(300$$^{\circ}$$)$$?

Accepted Answer

$$2$$

Question 17

If $$\cos(	heta) = \frac{1}{2}$$ and $$	heta is in $$the fourth quadrant, what is $$	heta$$?

Accepted Answer

$$330^{\circ}$$

Question 18

A satellite travels $$72,000 km in$$ $$3.5$$ hours. What is its average linear speed?

Accepted Answer

$$20,571 km/hr$$

Question 19

What is the value of $$\cot(135$$^{\circ}$$)$$?

Accepted Answer

$$-1$$

Question 20

If $$\sin(	heta) = 0.3210$$, what is $$	heta in $$radians (principal value)?

Accepted Answer

$$0.3268$$

Chapter 3: Radian Measure and the Unit Circle – Study Notes

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