Q. 6 - Precalculus Enhanced with Graphing Utilities

Question

On a circle of a radius $r$,a central angle of $\theta$ radians subtends an arc of length $s=\_\_\_\_\_\_\_\_$ ; the area of the sector formed by this angle $\theta$ is $A=\_\_\_\_\_\_\_\_$.

Step-by-Step Solution

Answer

The solution is $s=r·\theta$ , $A=\left(\frac{\theta }{360°}\right)\times {\mathrm{\pi r}}^2$ .

Step 1. Given information

The radius $r$ a circle and a central angle of $\theta$ radians

Step 2. Calculation

On a circle of a radius $r$,a central angle of $\theta$ radians subtends an arc of length $s=r·\theta$ ; the area of the sector formed by this angle  is $A=\left(\frac{\theta }{360°}\right)\times {\mathrm{\pi r}}^2$.