Question

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

Answer 1

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Polar form: `color(red)((r,theta)=(+-2, pi)`

Explanation:

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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.