Question

Calculate the angle of (a)$1^{\circ }$(degree) (b)$1^{\prime }$ (minute of arc or arc min) and (c)$1^{\prime \prime }$(second of arc or arc second) in radians.
Use ${360}^{\circ }=2\pi$ radian, $1^{\circ }={60}^{\prime }$ and $1^{\prime }={60}^{\prime \prime }$

Answer 1

We know that ${360}^{\circ }=2\pi$ radian

$\Rightarrow 1^{\circ }=\left(\frac{\pi }{180}\right)$ radian $=0.0175$ radian

$\Rightarrow 1^{\prime }=(\frac{1}{60}{)}^{\circ }=\frac{\pi }{60\times 180}$ radian $=0.00029$ radian

$\Rightarrow 1"=(\frac{1}{3600}{)}^{\circ }=\frac{\pi }{3600\times 180}$ radian $=0.0000048$ radian