Q. 122 - Precalculus Enhanced with Graphing Utilities

Question

For a circle of radius r, a central angle of u degrees subtends an arc whose length s is$s=\frac{\mathrm{\pi }}{180}r\theta$  . Discuss whether this is a true or false statement. Give reasons to defend your position.

Step-by-Step Solution

Answer

The statement is True.

Step 1. Given Information

The problem asks if the statement is true or false, "For a circle of radius $r$ , a central angle $\theta$, in degrees subtends an arc,$s$ whose length is equal to $s=\frac{\mathrm{\pi }}{180}r\theta$

Step 2. Reason for statement to be True or False

Since from the given formula of the arc length$s=\frac{\mathrm{\pi }}{180}r\theta$ , where the central angle$\theta$, is in degree, hence the statement is true . Analyzing, the degree unit will be cancelled out

leaving the unit in radians.