How do you convert the polar equation $theta=45^o$ into rectangular form?

Question

6644 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-10-31T16:09:32

Questions of the "How do you" type are best answered by explanation. Please see below.

Given:

$theta = 45°$

Substitute $tan^-1(y/x)$ for $theta$ but add the restriction $x > 0 and y > 0$

$tan^-1(y/x) = 45°; x > 0 and y > 0$

Take the tangent of both sides:

$tan(tan^-1(y/x)) = tan(45°);x > 0 and y > 0$

The tangent of its inverse returns $y/x$ and $tan(45°) = 1$

$y/x = 1;x > 0 and y > 0$

Multiply both sides by x and drop the restriction for y, because y is now dependent on x:

$y = x;x > 0$

How do you convert the polar equation theta=45^otheta=45^o into rectangular form?