Question #71435

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Answer 1 · 2018-02-04T17:22:29

#(2sqrt(34),0.5404)#

#(x,y)->(r,theta)#

We know that for a point #P# with coordinates #(x,y)#, that #x=rcos(theta)# and #y=rsin(theta)#

The angle #OP# makes with the x axis is therefore:

#sin(theta)/cos(theta)=y/x=tan(theta)=>theta=arctan(y/x)#

And:

#r=sqrt(x^2+y^2)#

We can use these ideas to convert Cartesian coordinates to polar coordinates.

#tan(theta)=y/x=6/10=3/5#

#theta=arctan(3/5)=0.54042color(white)(88)#radians.

#r=sqrt(x^+y^2)#

#r=sqrt((10)^2+(6)^2)=sqrt(136)=2sqrt(34)#

Polar coordinates:

#(2sqrt(34),0.5404)#