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

User Evamarie
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1 Answer

10 votes
10 votes

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

User Kajojeq
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