How do you convert #y = -x# into polar form?

Question

8258 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-06-10T05:14:43

Polar form of #y=-x# is #theta=(3pi)/4#

The relation between polar coordinates #(r,theta)# and Cartesian coordinates #(x,y)# is given by

#x=rcostheta#, #y=rsintheta# and #r^2=x^2+y^2#

As such #y=-x# can be written as

#rsintheta=-rcostheta# or

#(rsintheta)/(rcostheta)=-1# or

#tantheta=-1=tan((3pi)/4)# or

#theta=(3pi)/4#