Calculate the angle 1''(second of arc or arc of second) in radians.
please explain it a little elaborately

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Solution

To convert degrees to radians, first convert the number of degrees, minutes, and seconds to decimal form. Divide the number of minutes by 60 and add to the number of degrees. So, for example, 12° 28' is 12 + 28/60 which equals 12.467°. Next multiply by π and divide by 180 to get the angle in radians.

1` =1/60 degree
1``=1/3600 degree

0deg 0` 1``
So here Angle in radian =(0+0/60+1/6060) π/180=(1/3600)π/180

=4.8410^-6 radians

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

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