Question

Calculate the angle of a=1°, b=1', c= 1" in radians.

Answer 1

Answer 1) a=1° = 0.01745329252 radians

Explanation : According to the conversion chart, to convert 1° this formula is used;

radians = degrees × π / 180°

while solving for, One degree  which is equal 0.01745329252 radians:

1° = π/180° = 0.005555556π = 0.01745329252 rad

Answer 2) b = 1' =  = 0.0002907 radians

Explanation : A minute of arc is π/10800 of radian; which is a measurement unit of angular which is equal to 1/60 of 1° degree.

So substituting the value of 1°  as  and on solving we get,

0.01745/60 = 0.0002907 radians.

A minute of arc is π/10800 of a radian.

Answer 3) C= 1'' = 4.8481$X 10^{-6}$

Explanation - When calculating second of arc which is considered to be 1/60 of an arc minute, and 1/3600 of a degree; 

So all these are inter-related units which can be calculated if any one value is given;

on solving we get, π/648000 (about 1/206265) of a radian = 4.8481 X $10^{-6}$