# Radian Measure and Coterminal Angles

## Presentation on theme: "Radian Measure and Coterminal Angles"— Presentation transcript:

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.

To convert degrees to radians, multiply by To convert radians to degrees, multiply by

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

Radian Measure 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

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

Sketching Radians 90° 180° 360° 270°

Sketching Radians Trick: Convert the fractions into decimals and use the leading coefficients of pi

Example #1

Example #2

Example #3

Example #4

Experiment Graph and on the axes below. What do you notice?

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 Angles
If 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

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

Group Exit Ticket Are and coterminal? Why or why not?

Exit Ticket, cont. Multiply: Rationalize: