Question

The degree measure of 1 radian (taking $\pi =\frac{22}{7}$ ) is

• A. ${55}^o{61}^{{}^{\prime }}{22}^{\prime \prime }$ (approx.)
• B. ${57}^o{16}^{{}^{\prime }}{22}^{\prime \prime }$ (approx.)
• C. ${57}^o{22}^{{}^{\prime }}{16}^{\prime \prime }$ (approx.)
• D. ${57}^o{22}^{{}^{\prime }}{22}^{\prime \prime }$ (approx.)

Answer 1

The correct option is B ${57}^o{16}^{{}^{\prime }}{22}^{\prime \prime }$ (approx.)

$\pi radians={180}^{\circ }$

$1radian=\frac{180}{\pi }=\frac{180}{\frac{22}{7}}$

$1radian=57.272727$

The integer part constitutes the degree part. The mantissa is converted to minutes by multiplying with ${60}^{\prime }$

Minutes = $0.272727\ast {60}^{\prime }={16.3636}^{\prime }$

The integer part constitutes the minutes. The mantissa is converted to seconds by multiplying with ${60}^{\prime \prime }$

Seconds = $0.3636\ast {60}^{\prime \prime }\approx {22}^{\prime \prime }$

Hence, the degree measure of 1 radian is ${57}^{\circ }{16}^{\prime }{22}^{\prime \prime }$