Question

What is the measure in radians of the angle 0?

Answer 1

We can calculate the measure of the angle theta by the arc length formula:

`\text{Arc length= 2}\pi r((\theta)/(360))`

Substituing in the formula:

`\begin{gathered} 6=2\pi(4)((\theta)/(360)) \\ \text{Isolating the variable }\theta\colon \\ \theta=(6\cdot360)/(2\pi\cdot4) \\ \theta=85.94\text{ degrees} \end{gathered}`

To convert the angle to radians:

`\begin{gathered} \theta\cdot(\pi)/(180)=x\text{ rad} \\ 85.94\cdot(\pi)/(180)=1.5\text{ rad} \end{gathered}`