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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
Radian Measure
3.57π180
radian
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
Trick: Convert the fractions into decimals and use the leading coefficients of pi
2π π π2
2π3
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