Quick Math Fix #4
Radians vs. Degrees
Radians are included on the SAT reference sheet, but a lot of students still have no idea what they are—or how to convert between radians and degrees.
Let’s fix that.
What’s a Radian?
A radian is a way to measure angles based on the arc length of a circle. While degrees (º) divide a circle into 360 equal parts, radians use the radius as the unit of measure.
Converting Between Degrees and Radians
You really need to remember only one thing:
From that, you can build the two formulas:
To convert to degrees:
\(\text{Radians}\times\frac{180}{\pi}\)To convert to radians:
\(\text{Degrees}\times\frac{\pi}{180}\)
Quick trick: If you're converting radians to degrees, you can just plug in π = 180º to get the answer.
Example
The Quick Test
If you're ever unsure whether you've converted correctly, use this logic check:
If you're converting to degrees, your answer should be bigger than the radian value (unless you're dealing with decimals or very small fractions).
If you're converting to radians, your answer should include π.
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Love that Elmo image!