Radian Measure and Coterminal Angles

Take out your homework from

Friday!!!

Warm-up (1:30 m) Using your “Degrees and Radians” handout

from Friday, describe how you convert between degrees and radians.

Converting Between Degrees and Radians

To convert degrees to radians, multiply by

To convert radians to degrees, multiply by

Converting Between and Radians, cont

Degrees → Radians Radians → Degrees

2205π

Picture of Unit Circle with missing degrees and radian measures. Students fill missing measures.

Radian Measure

3.57π180radian

Another way of measuring angles Convenient because major measurements of a

circle (circumference, area, etc.) are involve pi Radians result in easier numbers to use

Radian Measure, cont.

The Unit Circle – An Introduction Circle with radius of 1 1 Revolution = 360°

2 Revolutions = 720° Positive angles move

counterclockwise around the circle

Negative angles move clockwise around the circle

0°

90°

180°

270°

360°

Sketching Radians

Sketching Radians Trick: Convert the fractions into decimals

and use the leading coefficients of pi

2π π π2

2π3

Example #1 6π5

Example #2 4π6

Example #3 4π

Example #4 7π9

Your Turn:7π12

3π

Your Turn:7π10

3π5

Your Turn:13π15

9π17

ExperimentGraph and on the axes below. What

do you notice?23

2

Coterminal Angles

co – terminal

Coterminal Angles – angles that end at the same spot

with, joint, or together

ending

Coterminal Angles, cont. Each positive angle has a negative

coterminal angle Each negative angle has a positive

coterminal angle

Solving for Coterminal AnglesIf the angle is

greater than 2 pi, subtract 2 pi from the given

angle.

If the angle is less than 0, add 2 pi

to the given angle.

You may need to add or subtract 2 pi more than once!!!

Trick: Add or subtract the coefficients of pi rather than the entire radian measure

Examples: Find a coterminal angle between 0 and 2 pi

6π293π2

Your Turn: Find a coterminal angle between 0 and 2 pi

5π18

13π14

4π9

4π6

Group Exit Ticket Are and coterminal? Why or

why not?

6π7

6π17

Exit Ticket, cont.

1. Multiply:

2. Rationalize:22

18*2