Radian Measure and Coterminal Angles
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Transcript of Radian Measure and Coterminal Angles
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