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