Question

Find radian measure from degree ?
$-{47}^{\circ }{30}^{\prime }$

• A. $0.729$
• B. $-0.829$
• C. $0.629$
• D. $0.529$

Answer 1

The correct option is B $-0.829$

${47}^{\circ }{30}^{\prime }$

$-\left({47}^{\circ }+{30}^{\prime }\right)$

$-\left({47}^{\circ }+\frac{{30}^{\circ }}{60}\right)$ $1\mathrm{deg}ree=60min$

$-\left({47}^{\circ }+\frac{1^{\circ }}{2}\right)$ $1^{\circ }={60}^{\prime }$

$-\left(\frac{94+1}{2}\right)$ $1^{\prime }=\frac{1}{{60}^{\circ }}$

$-\left(\frac{{95}^{\circ }}{2}\right)$ ${30}^{\prime }=\frac{30}{{60}^{\circ }}$

$NowRadianMeasure=\frac{\pi }{180}\times DegreeMeasure$

$=\frac{\pi }{180}\times \left(\frac{-{95}^{\circ }}{2}\right)$

$=\pi \times \frac{-19}{72}$

$=\frac{-19\pi }{72}radians\approx -0.829$