Q. 5 - Precalculus Enhanced with Graphing Utilities

Question

If the radius of a circle is $r$ and the length of the arc subtended by a central angle is also $r$, then the measure of the angle is $1\_\_\_\_\_\_\_$.

Step-by-Step Solution

Answer

The solution is radian .

Step 1. Given information

Radius of a circle is $r$ and the length of the arc subtended by a central angle is also $r$.

Step 2. Calculation

For a circle of radius $1$, the rays of a central angle with measure $1$ radian subtend an arc of length $1$. For a circle of radius $3$ the rays of a central angle with measure $1$ radian subtend an arc of length $3$.

So, if radius of a circle is $r$ and the length of the arc subtended by a central angle is also $r$, then the measure of the angle is $1$ radian.