How do you convert #(-2,0)# from cartesian to polar coordinates?

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Given:

Cartesian coordinates: #color(blue)((-2,0)#

How do we convert from Cartesian coordinates to Polar form?

Polar Form: #color(blue)((r, theta)#

Examine the sketch below:

Important formula to remember:

#color(blue)(x^2+y^2=r^2#

#color(blue)(tan(theta)=y/x#

#color(blue)(cos(theta)=x/r rArr x = r cos(theta)#

#color(blue)(sin(theta)=y/r rArr y = r sin(theta)#

Let us identify the point on the Cartesian Plane:

Cartesian coordinates: #color(blue)((-2,0)#

Note that the angle is #pi#

Hence #color(red)(theta = pi#

Use the formula: #color(blue)(x^2+y^2=r^2#

#rArr (-2)^2+(0)^2=r^2#

Swap sides:

#rArr r^2=(-2)^2+(0)^2#

#rArr r^2=4+0#

#rArr r^2=4#

Taking the #color(red)(sqrt# on both sides:

#rArr sqrt(r^2)=sqrt(4)#

#rArr r=+-sqrt(4)#

#rArr r=+-2#

Hence, the required Polar form: #color(red)((+-2, pi)#

Hope this helps.