Answered

At Westonci.ca, we connect you with the best answers from a community of experienced and knowledgeable individuals. Explore thousands of questions and answers from knowledgeable experts in various fields on our Q&A platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

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

Sagot :

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

[tex]180^0=\pi radians[/tex]

So

[tex]1^0=\frac{\pi}{180^}radian[/tex]

Then

[tex]\begin{gathered} D^0=D\times\frac{\pi}{180}radian \\ D^0=\frac{D\pi}{180}radians \end{gathered}[/tex]

Therefore

[tex]\frac{D\pi}{180}=R[/tex]

Let us divide both sides by pie

[tex]\frac{D\pi}{180}\div\pi=R\div\pi[/tex]

[tex]\begin{gathered} \frac{D\pi}{180}\times\frac{1}{\pi}=R\times\frac{1}{\pi} \\ \frac{D}{180}=\frac{R}{\pi} \end{gathered}[/tex]

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

We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.