Write as polar coordinates( 2,2)?

1 Answer
Nov 11, 2017

Polar coordinates are #(sqrt8,pi/4) #

Explanation:

Let polar coordinates be #(r,theta) # and Cartesian co ordinate

is #(2,2) :. x=2,y=2#. We know #x=r cos theta and y=r sin theta#

#:. 2=r cos theta; (1) and 2=r sin theta; (2) # .Squaring we get

#:. 4=r^2 cos^2 theta and 4=r^2 sin^2 theta # , Adding both we get,

#:. 8=r^2 (cos^2 + sin^2 theta) or r^2=8 [sin^2theta+cos^2 theta=1] #

#:. r = sqrt 8# . Dividing equation (2) by equation (1) we get

#tan theta =1 ; tan (pi/4)=1 :. theta= pi/4#

Therefore polar coordinates are #(sqrt8,pi/4) # [Ans]