Question

How do you convert r = $\cos \theta$ in rectangular form?

Answer 1

In the above question you have to convert r = $\cos \theta$ in rectangular form. A standard rectangular form looks like ${x^2} + {y^2} = {r^2}$ . Also, for converting a rectangular form into polar form, we take $x = r\cos \theta$ and $y = r\sin \theta$ . So let us see how we can solve this problem.

Complete step-by-step answer:
In the given question we have to convert r = $\cos \theta$ in rectangular form. We know that the standard rectangular equation looks like ${x^2} + {y^2} = {r^2}$ .
We have r = $\cos \theta$
If we multiply both the sides of the above equation with r, then we get
$\Rightarrow {r^2} = r\cos (\theta )$
Now, using the formula of standard rectangular form that is ${x^2} + {y^2} = {r^2}$ and $x = r\cos (\theta )$ , we get
$\Rightarrow {x^2} + {y^2} = x$
Therefore, r = $\cos \theta$ can be written in rectangular form as ${x^2} + {y^2} = x$ .

Note: In the above solution we used a rectangular equation that is ${x^2} + {y^2} = {r^2}$ . Polar coordinates come in form of $(r,\theta )$ while rectangular coordinates come in form of (x, y). A rectangular form is also called the Cartesian form.