Convert this to a rectangular equation θ = π/4 ?

Question

Write the polar equation as a rectangular equation. Express with variables on the left.

That is what your supposed to do for that problem but I don't know how, so could some one please help me. Thanks.

Answer 1

y=x with x>0

Answer 2

tan(θ)= y/x

then since: tan(π/4)=1
this is the same thing as
tan(π/4)= 1/1
So... 1/1 would be the slope of the line crossing through the oringin. The equation of such line is y=x.

I saw a person said that the answer should be x>0, but when you graph an angle like θ = π/4 the polar graph gives a line throught the pole in both directions... this translated to rectangular coordinates says that the answer is in the interval
(-∞,+∞).

Answer 3

Take the tangent of each side:

tan θ = tan π/4

tan θ = 1

y/x = 1
y = x
y-x = 0 if you want all the variables on the left.

The domain is all real numbers, there are no restrictions, because in polar form, the line θ = π/4 can have positive and negative values for r, so points in quadrant I and quadrant III are graphed.