1. What is 311° in radians?
Have you ever wondered how to find the radian equivalent of an angle like 311 degrees?

3. Recall from an earlier lesson that pi radians is equivalent to 180 degrees.

4. of the circumference 2πr
arclength, s s= θ 360 2πr θ
of the circumference 2πr
s r = θ π 180
You may also recall from Geometry the formula for finding the length of an arc where the angle theta is measured in degrees; if we divide by r and simplify we get s/r = θ*π/180

5. s r = θ π 180 θ
s r = θ
Compare that result with degree measure to our definition of radian measure: θ = s/r
Notice the only difference between these equations? s/r must be equal to itself… so that tells us that θ π 180 where theta is degree measure must be equal to theta in radian measure.
In other words, if you multiply degrees by π 180 you will get radians.

6. π 180° = 1 1 = 180° π π 180° This makes sense because we know π=180°
π 180° = 1
1 = 180° π
This makes sense because we know π=180°
If we divide this equation by 180 we get π 180 =1 which is what we multiply by to change degrees to radians. Notice that we are multiplying by 1, so it doesn’t change the angle measure.
Likewise, we could divide our equation by pi to get 180 π =1. This is what we multiply by to change radians to degrees.

7. 190° 72° −145° 2 5π/18 -3
Which of these angle measures is in degrees and which are in radians? Some students think that if they don’t see “pi” in the angle then the angle is in degrees when in fact they should be looking for the ° symbol to determine if it is degrees.
In these examples, only the first three are in degrees, while the last three are all radians.

8. Convert the following angles given in degrees, to radians
Convert the following angles given in degrees, to radians. Round to the nearest hundredth of a radian.
a) 311◦ b) 54◦ c) −75◦.
Convert the following angles given in degrees, to radians. Round to the nearest hundredth of a radian.
a) 311◦ b) 54◦ c) −75◦.
[Use the Bamboo during recording. Discuss exact values that are in terms of pi AND approximate rounded values in the last example only, -75Type equation here..]

9. Convert the following radian measures to degrees
Convert the following radian measures to degrees. Round to the nearest degree.
a) 3 b) 5π 12 c) -2
[Use the Bamboo during recording. Discuss exact values that are in terms of pi AND rounded values in the second example.]