Question

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

Answer 1

use concept,

$360°=2\pi$ rad

$1°=2\pi /360=\pi /180$ rad

$1^{\prime }$ ( it means minute )

$60$ minutes $\left({60}^{\prime }\right)=1°$

$1$ minute $=1/60°$

but $1°=\pi /180$ rad

so, $1/60°=\pi /60\times 180=\pi /10800$ rad

$1^{\prime \prime }=?$ rad

${60}^{\prime \prime }=1$ minute

and ${60}^{\prime }=1°$ so, ${3600}^{\prime \prime }=1°$

so, $1^{\prime \prime }=\pi /180\times 3600=\pi /648000$ rad.