4.1 Radian and Degree Measure

4.2 Radian and Degree Measure

Multiple Choice

What does the word "trigonometry" literally mean?

• Rotation of lines

• Calculation of angles

• Measurement of triangles

• Study of circles

Multiple Choice

Which statement about angle rotation is correct?

• Positive angles rotate clockwise

• Negative angles rotate counterclockwise

• Positive angles rotate counterclockwise

• All angles rotate in the same direction

Multiple Choice

Coterminal angles are angles that:

• Have the same length

• Form a right angle

• Rotate in opposite directions

• Have the same initial and terminal sides

Radian Measure

Radian: An angle measurement based on the radius

ways of measuring angles

1- Degree Measure:

• ​Full circle = 360 degrees

• Right angle = 90 degrees

• Straight angle = 180 degrees

2- Radian Measure:

• ​Full circle = 2π radians

• Half circle = π radians

Multiple Select

Determine two coterminal angles (one positive and one negative) for each angle. (Choose 2 answers)

• $$\frac{8\pi}{3}$$

• $$-\frac{7\pi}{3}$$

• $$\frac{5\pi}{3}$$

• $$-\frac{5\pi}{3}$$

Multiple Select

Determine two coterminal angles (one positive and one negative) for each angle. (Choose 2 answers)

• $$\frac{\pi}{4}$$

• $$-\frac{7\pi}{4}$$

• $$\frac{5\pi}{4}$$

• $$-\frac{5\pi}{4}$$

Multiple Choice

Which of the following angles are co-terminal to 330^o?

• -330^o, 330^o

• 510^o, -210^o

• 690^o, -30^o

• 420^o, -330^o

Multiple Choice

Which of the following angles are co-terminal to -75^o?

• -365^o, 75^o

• 285^o, -435^o

• 105^o, -255^o

• 425^o, -335^o

Multiple Choice

Which of the following angles are co-terminal to 450^o?

• 450^o, -450^o

• 90^o, -270^o

• 270^o, -90^o

• 420^o, -330^o

Multiple Choice

Which quadrant is -570⁰

• I
• II
• III
• IV

Multiple Choice

Negative angles are measured in which direction from standard position?

• Clockwise
• Counterclockwise

Multiple Choice

Which of the following shows $$-210\degree$$  graphed in standard position?

Multiple Choice

Find (if possible) the complement of $$\frac{\pi}{6}$$

• $$\frac{\pi}{5}$$

• $$\frac{\pi}{3}$$

• $$\frac{5\pi}{6}$$

• none

Multiple Choice

Find (if possible) the supplement of $$\frac{\pi}{6}$$

• $$\frac{\pi}{5}$$

• $$\frac{2\pi}{3}$$

• $$\frac{5\pi}{6}$$

• none

Multiple Choice

Find (if possible) the complement of $$\frac{5\pi}{6}$$

• $$\frac{\pi}{5}$$

• $$\frac{2\pi}{3}$$

• $$\frac{5\pi}{6}$$

• none

Multiple Choice

Find (if possible) the supplement of $$\frac{5\pi}{6}$$

• $$\frac{\pi}{6}$$

• $$\frac{\pi}{4}$$

• $$\frac{\pi}{3}$$

• none

Multiple Choice

• 60^o

• 157^o

• 50^o

• 493^o

Multiple Choice

FIND THE ARC LENGTH OF THE BOLDED ARC

• A
• B
• C
• D

Multiple Choice

Find the area of each sector.

• 52.4 in²
• 18,864 in²
• 60 in2
• 10.47 in

Multiple Choice

What is the area of the shaded sector?

• 339.12 in²
• 113.04 in²
• 339.29 in²
• None of the above

Degree Measure

​A second way to measure angles is in degrees, denoted by the symbol °.

Multiple Choice

Convert each degree measure to radian measure as a multiple of π. Do not use a calculator.

a) 60⁰

• π/4

• π/3

• π/6

• π/9

Multiple Choice

Convert each degree measure to radian measure as a multiple of π. Do not use a calculator.

a) 320⁰

• 14π/9

• 16π/9

• 11π/9

• 17π/9

Multiple Choice

Convert each radian measure to degree measure. Do not use a calculator.

a) π / 6

• 30°

• 60°

• 45°

• 55°

Multiple Choice

Convert each radian measure to degree measure. Do not use a calculator.

a) 5π / 3

• 270°

• 320°

• 280°

• 300°

Multiple Choice

What is 225  degrees in radians? 

• 7π/4
• 5π/4
• 3π/4
• 5π/3

Multiple Choice

Convert 100⁰ to radians

• 5π/9
• π/2
• 5π/8
• 5π/6

Multiple Choice

Convert -40^o into Radians

• -4π / 8

• -8π / 9

• -2π / 9

• -5π / 8

Multiple Choice

$$Convert\ \frac{15\pi}{4}rad\ to\ Degree\ Measure.$$  

• $$665\degree$$  

• $$670\degree$$  

• $$675\degree$$  

• $$680\degree$$  

Multiple Choice

$$Convert\ \frac{11\pi}{60}rad\ to\ Degree\ Measure.$$  

• $$44\degree$$  

• $$33\degree$$  

• $$55\degree$$  

• $$66\degree$$  

Multiple Choice

$$Convert\ -27\degree\ to\ Radian\ Measure.$$  

• $$-\frac{5\pi}{22}rad$$  

• $$-\frac{4\pi}{21}rad$$  

• $$-\frac{3\pi}{20}rad$$  

• $$-\frac{2\pi}{19}rad$$