Question

Radian of 66°2minute 40 second?

Answer 1

`66° 2' 40''= 1.15192377 ["rad"]`

Explanation:

`(alpha [°])/360=(alpha ["rad"])/(2 pi)`
`=> alpha["rad"]=alpha[°] (2 pi)/(360)=alpha[°] pi/180`

`66° 2' 40''=(66 + 2/60 +40/3600)°=66.00037037°=`
`=66.00037037° * pi/180 = 1.15192377 ["rad"]`

Answer 2

`1.153` radians to 3 decimal places approximately

`743/2025xxpi` radians exactly

Explanation:

`color(blue)("Known facts")`

minute `= 1/60` of a degree `->66+2/60`
second `=1/60` of a minute which is `1/60xx1/60 = 1/3600` of a degree `->66+2/60+40/3600` degrees in total.

There are `pi` radians in `180^o`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Using the known constants to answer the question")`

So we have:

`[(66+2/60+40/3600)/180xxpi]` radians =`1.152693...` radians

`1.153` radians to 3 decimal places approximately

`743/2025xxpi` radians exactly