Quick Review Lesson: Angles, Arcs, and Sectors

Quick Review Lesson: Angles, Arcs, and Sectors

Standard position

Multiple Choice

Which of the following is a negative coterminal angle of 165 degrees?

• 195

• 525

• -525

• -195

Multiple Choice

In which quadrant would you find an angle measuring -740°

• 1

• 2

• 3

• 4

Multiple Choice

Find a coterminal angle to -27°.

• -387°

• 27°

• 323°

• -393°

Multiple Choice

What is the degree measure of this angle?

• -230^o

• -590^o

• -490^o

• 590^o

Multiple Choice

The terminal side of a -45° angle is in what Quadrant?

• Quadrant I

• Quadrant II

• Quadrant III

• Quadrant IV

Multiple Choice

Which of the following shows  $480\degree$  graphed in standard position?

Multiple Choice

Which of the following shows  $300\degree$  graphed in standard position?

45 degrees is the REFERENCE ANGLE for 45, 135, 225, and 315

It's always acute!

• Determine the rotational distance between your angle and the x-axis

• The reference angle is ALWAYS going to be acute...otherwise you did something in error

• 73 deg is the reference angle for 253

Multiple Choice

What is the reference angle?

• 112

• 68

• 158

• 248

Multiple Choice

What is the reference angle for -310⁰?

• 50⁰

• -50⁰

• 20⁰

• 40⁰

Multiple Choice

What is the reference angle for 125°?

• 235°

• 125°

• 75°

• 55°

Degrees to Radians

• Angles can be measured in degrees or radians

• Sometimes, it's necessary to convert from one to the other

• Use conversion factor (yellow) or proportional reasoning

Multiple Choice

How many radians are in $60\degree$ ?

•  $\frac{\pi}{2}$  

•  $\frac{3\pi}{2}$  

•  $\frac{\pi}{3}$   

Multiple Choice

What is 4π/3 radians in degrees?
 

• 120
• 240
• 210
• 270

Multiple Choice

What is 150 degrees in radians?

• 5π/6
• 7π/6
• 5π/4
• π/6

Multiple Choice

How many degrees are in $\frac{5\pi}{4}$   radians?

•  $270\degree$  

•  $225\degree$  

•  $180\degree$  

Multiple Choice

Convert the following to radians:   
720⁰

• 3π
• 4π
• 5π

Multiple Choice

Find the arc length. Leave your answer in terms of π.

• 7/4π

• 7/2π

• 1/8π

• 45π

Multiple Choice

When she is outdoors, Tasha, the dog, is tied to a stake in the center of a circular area of radius 24 feet. The angle between her dog house and her favorite hydrant is 165 degrees. What is the length of the arc from her dog house to the hydrant, following minor arc DG, to the nearest foot.

• 40

• 35

• 55

• 69

Multiple Choice

Alison is jogging on a circular track that has a radius of 140 feet. She runs along the track from point R to point N, a distance of 230 feet. Find to the nearest degree, the measure of angle RUN:

• 47

• 74

• 94

• 123

Multiple Choice

is the formula for?

• arc length
• area of a sector
• area of a segment
• arc measure

Multiple Choice

Find the area of the shaded sector of circle O. The radius is 6 inches and the central angle is 100°. Express answer as an exact value

• 5π/3

• 10π/3

• 10π

• 40π

Multiple Choice

What is the area of sector​ GPH?

• 9π yd²

• 32π yd²

• 18π yd²

• 6π yd²

Multiple Choice

Find the area of each sector.

• 52.4 in²

• 18,864 in²

• 60 in2

• 10.47 in