http://www.ck12.org Chapter 4. Basic Triangle Trigonometry
360 degrees= 2 πradians, so^180 π degrees= 1 radian
Alternatively; 360degrees= 2 πradians, so 1degree= 180 π radians
The conversion factor to convert degrees to radians is: 180 π◦
The conversion factor to convert radians to degrees is:^180 π◦
If an angle has no units, it is assumed to be in radians.
Example A
Convert 150◦into radians.
Solution: 150 ◦· 180 π◦=^1518 π=^56 πradians
Make sure the degree units cancel.
Example B
Convertπ 6 radians into degrees.
Solution:π 6 ·^180 π◦=^1806 ◦= 30 ◦
Often theπ’s will cancel.
Example C
Convert( 6 π)◦into radians.
Solution:Don’t be fooled just because this hasπ. This number is about 19◦
( 6 π)◦· 180 π◦=^6180 π^2 =π 32
It is very unusual to ever have aπ^2 term, but it can happen.
Concept Problem Revisited
Exactly 2πradians describe a circular arc. This is because 2πradiuses wrap around the circumference of any circle.
Vocabulary
Aradianis defined to be the central angle where the subtended arc length is the same length as the radius.
Asubtended arcis the part of the circle in between the two rays that make the central angle.
Guided Practice
- Convert^56 πinto degrees.
- Convert 210◦into radians.
- Draw aπ 2 angle by first drawing a 2πangle, halving it and halving the result.
Answers:
1.^56 π·^180 π◦=^5 ·^301 ◦= 150 ◦ - 210◦· 180 π◦=^76 ·^30 · 30 ·π=^76 π
3.π 2 = 90 ◦