Question

If D and R denote the degree and radian measure of an angle, then prove that D/180=R/pie

Answer 1

Given: D and R denote the degree and radian measure of an angle

To Determine: The prove that D/180=R/pie​

Solution

Please note that

`180^0=\pi radians`

So

`1^0=(\pi)/(180^)radian`

Then

`\begin{gathered} D^0=D*(\pi)/(180)radian \\ D^0=(D\pi)/(180)radians \end{gathered}`

Therefore

`(D\pi)/(180)=R`

Let us divide both sides by pie

`(D\pi)/(180)/\pi=R/\pi`

`\begin{gathered} (D\pi)/(180)*(1)/(\pi)=R*(1)/(\pi) \\ (D)/(180)=(R)/(\pi) \end{gathered}`

Hence, the above help to prove that D/180 = R/pie