Question

The Degree Measure of $1radian$ Is (Taking$\mathrm{\pi }=\frac{22}{7}$)

Answer 1

Step 1: Conversion of $1radian$in degree.

Since $\mathrm{\pi }radian={180}^{°}$

Therefore $1radian=\frac{{180}^{°}}{\mathrm{\pi }}$

$\Rightarrow$ $$\begin{gathered} 1radian=\frac{180}{22}x7 \\ =57.272727° \end{gathered}$$

Step 2: Conversion of degree to minutes.

Since The integer part constitute the degree part.The mantissa is converted to minutes by multiplying with $60\text{'}$.

Therefore $minutes=0.272727x60=16.3636\text{'}$

Step 3: Conversion of minutes to seconds.

Since The integer part constitute the minutes part.The mantissa is converted to seconds by multiplying with $60\text{'}$.

Therefore $second=0.3636x60\approx 22\text{'}\text{'}$
Hence, the degree measure of $1radian$ is $57°16\text{'}22\text{'}\text{'}$