Radian of 66°2minute 40 second?

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Answer 1 · 2018-04-21T18:28:36

#66° 2' 40''= 1.15192377 ["rad"]#

#(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 · 2018-04-21T18:41:44

#1.153# radians to 3 decimal places approximately

#743/2025xxpi# radians exactly

#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