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Six Trigonometric Functions and Radians

Degrees versus radians and calculator modes.

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Radian Measure

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You probably are familiar with degrees in trig, but did you know there is another way to measure angles?

These are called Radians and unlike Degrees, do not have a unit.

Why don't radians have a unit? How are they derived? Look here for guidence

Converting Between Radians and Degrees 

.\begin{align*}\pi Radians=180^\circ \end{align*}πRadians=180

To go from degrees to Radians multiply your degrees by \begin{align*}\frac{\pi}{180^\circ }\end{align*}π180

To go from Radians to degrees multiply your radians by \begin{align*}\frac{180^\circ }{\pi}\end{align*}180π

Tips and Tricks: Since we know that \begin{align*}\pi=180^\circ \end{align*}π=180, you can visualize \begin{align*}\pi\end{align*}π radians as being half a circle. Using this trick, fill out the table below.

Radians Degrees
\begin{align*}\frac{\pi}{2}\end{align*}π2
\begin{align*}\frac{\pi}{3}\end{align*}π3
\begin{align*}\frac{\pi}{4}\end{align*}π4
\begin{align*}\frac{\pi}{6}\end{align*}π6

Note: In upper level math Radians are prefered over degrees because they are unitless, so you should get used to Radians!

For extra practice, try these practice problems here.

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