Radian Measure and Coterminal Angles

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Presentation transcript:

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

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

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

Sketching Radians 90° 0° 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

Your Turn:

Your Turn:

Your Turn:

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: