Calculate the angle of (a) `1^(@)` (degree) (b) 1' (minute of arc or arcmin) and `("c")` 1" (second of arc or arc second ) in radians. Use `360^(@) = 2pi` rad, `1^(@)=60'` and 1'=60".

Explanation

(a)We know that,
`180^(@)= pi` rad
then `1^(@)=(?)`
`:.1^(@)=(pi)/(180)=(3.412)/(180)`
`:.1^(@)=0.01745`
`:.1^(@)~~1.745xx10^(-2)` rad
(b) We know that,
`60.(min)=1^(@)`
and `1^(@)=1.745xx10^(-2)` rad
`:.60.=1.745xx10^(-2)` rad
`:. 60.=1.745xx10^(-2)` and
then `1.=(?)`
`1=(1.745xx10^(-2))/(60)=0.02908xx10^(-2)`
`:.1=2.91xx10^(-4)` rad
We know that,
`60..(sec)=1.(min)`
`and 1.(min)=2.908xx10^(-4)` rad
`:. 60..=2.908xx10^(-4)` rad
then `1,,=(?)`
`I..=(2.908xx10^(-4))/(60)=0.048466xx10^(-4)`
`:.1..~~4.85xx10^(-6)` rad