How do you convert (-5,0) to polar form?

1 Answer
Dec 15, 2017

(5,pi)

Explanation:

Using:

x=rcostheta

y=rsintheta

theta=arctan(y/x)

From example:

-5=rcosthetacolor(white)(88)[1]

0=rsinthetacolor(white)(8888)[2]

Squaring [1] and [2]:

25=r^2cos^2theta

0=r^2sin^2theta

Adding [1] and [2]:

25=r^2cos^2theta+r^2sin^2theta

Factor:

25=r^2(cos^2theta+sin^2theta)

25=r^2=> r=+-5 ( use r=5 )

For r=5:

y=0=5sintheta=>sintheta=0

x=-5=5costheta=>costheta=-1

theta=arctan(sintheta/costheta)=0/-1= , pi

Polar coordinates:

(5,pi)