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Exercises Trigonometry

Example 2 from Algebra and Trigonometry, 7.1 Angles

Finding a Radian Measure

Find the radian measure of one-third of a full rotation.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
For any circle, the arc length along such a rotation would be one-third of the circumference. We know that

$1 rotation = 2 π r$

So,

$\begin{matrix} s & = & \frac{1}{3} (2 π r) \\ = & \frac{2 π r}{3} \end{matrix}$

The radian measure would be the arc length divided by the radius.

$\begin{matrix} radian measure & = & \frac{\frac{2 π r}{3}}{r} \\ = & \frac{2 π r}{3 r} \\ = & \frac{2 π}{3} \end{matrix}$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Find the radian measure of three-fourths of a full rotation.

How did it go?

PreviousDrawing an Angle in Standard Position Measured in Degrees Next Converting Radians to Degrees

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 7.1, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.