Radian of 66°2minute 40 second?

2 Answers
Apr 21, 2018

#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"]#

Apr 21, 2018

#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