Question

How do you change the polar equation `theta+pi/3=0` into rectangular form?

Answer 1

`theta` is a constant, `-pi/3`, but r is allowed to be any value from `-oo" to "oo`; this defines a line. Substitute `tan^-1(y/x)` for `theta` and then solve for the resulting line.

Explanation:

Given: `theta + pi/3 = 0`

Subtract `pi/3` from both sides:

`theta = -pi/3`

Substitute `tan^-1(y/x)` for `theta`:

`tan^-1(y/x) = -pi/3`

Use the tangent function on both sides:

`y/x = tan(-pi/3)`

Multiply both sides by x:

`y = tan(-pi/3)x`

Here is a graph of the function: