How do you graph $r = 2$ $r = 2$ ?

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How do you graph $r = 2$ $r = 2$ ?

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Answer 1 · 2015-12-13T23:20:26

You can change it to rectangular coordinates or consider that is the graph produced by a point at distance $2$ $2$ from the origin and at all the possible angles $θ$ $theta$ from the positive $x$ $x$ axis (and so describing a circle!).

Explanation:

Consider the following diagram:

enter image source here
We can see that the relationships between rectangular and polar coordinates are:
$r = \sqrt{x^{2} + y^{2}}$ $r=sqrt(x^2+y^2)$
$θ = arctan (\frac{y}{x})$ $theta=arctan(y/x)$
and:
$x = r cos (θ)$ $x=rcos(theta)$
$y = r sin (θ)$ $y=rsin(theta)$

In your case you have:
$r = 2$ $r=2$
Change it into rectangular to get:
$\sqrt{x^{2} + y^{2}} = 2$ $sqrt(x^2+y^2)=2$
Square both sides:
$x^{2} + y^{2} = 2^{2}$ $x^2+y^2=2^2$
Which is the equation of a circle of radius $2$ $2$ and centred in the origin.

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How do you graph $r = 2$ $r = 2$ ?

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