Question

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

Answer 1

We know that ${360}^0=2\pi rad$

$\Rightarrow 1^0=\left(\frac{\pi }{180}\right)rad=0.0175rad$

$\Rightarrow 1^{\prime }=\left(\frac{1}{60}\right)=\frac{\pi }{60\times 180}=0.00029rad$

$\Rightarrow 1"=\left(\frac{1}{3600}\right)=\frac{\pi }{3600\times 180}=0.0000048rad$