If D, G and R Denote Respectively the Number of Degrees, Grades and Radians in an Angle Then

Question:

If \(D\), \(G\) and \(R\) denote respectively the number of degrees, grades and radians in an angle, then

(a) \(\frac{D}{100} = \frac{G}{90} = \frac{2R}{\pi}\)

(b) \(\frac{D}{90} = \frac{G}{100} = \frac{R}{\pi}\)

(c) \(\frac{D}{90} = \frac{G}{100} = \frac{2R}{\pi}\)

(d) \(\frac{D}{90} = \frac{G}{100} = \frac{R}{2\pi}\)

Solution

We know that:

\[ 180^\circ = 200 \text{ grades} = \pi \text{ radians} \]

Dividing throughout by \(2\):

\[ 90^\circ = 100 \text{ grades} = \frac{\pi}{2} \text{ radians} \]

Therefore,

\[ \frac{D}{90} = \frac{G}{100} = \frac{R}{\pi/2} \]

\[ \frac{D}{90} = \frac{G}{100} = \frac{2R}{\pi} \]

Hence, the correct option is:

(c) \( \frac{D}{90} = \frac{G}{100} = \frac{2R}{\pi} \)