How to convert 10 radian in degree minutes and seconds ?

3 Answers
May 16, 2018

#572^@ 57'36''#

Explanation:

  1. converting to degree : ( Multiply by #180/pi# )
    #10xx180/pi=572. color(red)(96)^@#

  2. converting to minutes :( #color(red)(0.96) xx 60# )
    #color(white)(.)#
    #0.96xx60=57. color(blue)(6)#

  3. converting into seconds : ( #color(blue)(0.6) xx 60# )
    #color(white)(.)#
    #0.6xx60=36#

So , #10# radians #=572^@ 57'36''#

May 16, 2018

10 rad #~~ 572^@57'28#

Explanation:

We need to know what a radian is to answer this. An angle with an arc that has the same length as the radius of a circle is called a radian. As the circumference of a circle with radius = 1 har a length of #2pi#, it follows that #π# rad = #180°#

Therefore 10 rad = #(180^@*10)/pi = 572.95779513^@#

As there are #60'# in #1^@# and #60#” in #1'#, we get
#0.95779513^@=0.95779513*3600##~~3448##=57'28#

Therefore we get:
10 rad #~~ 572^@57'28#

Please note that this is more than one time around the circle, by the way.

And by the way, please note that the discrepancy between my and @Evan's answer is due to the level of accuracy used.

May 16, 2018

#572^o color(white)("..")57^("'") color(white)("..")28^("''")# to the nearest second

Explanation:

#color(red)("Important fact: there are "2pi" radians in a circle")#

So #ul("1 radian")# in degrees is #360/(2pi) = 180/pi" degrees"#

We have 10 radians so the count of degrees is

#10xx180/pi = 1800/pi" Degrees" ~~ 572.957795....#

Store this in your calculator memory to reduce rounding errors.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
So the degrees part of the measure is: #572^o#

The minutes part is #(1800/pi-572)xx60 = 57.467..=57^'#

The second's part is:
#(1800/pi-572-57/60)=7.79513...xx10^-3" degrees" #

Convert this into seconds: #7.79513...xx10^-3-:1/(60^2)=28.0624.... "seconds"#

So the answer is: #572^o color(white)("..")57^("'") color(white)("..")28^("''")# to the nearest second