How do I write θ=11π/6 as an equation in rectangular coordinates?

Question

I could really use help understanding how to get to the answer. Thanks.

Answer 1

The first step to converting this into rectangular coordinates is to take the tangent of the angle of both sides, tan(theta)=tan(11*pi/6). Next, consider tan(theta)=y/x. Then, this implies y/x=(-1/2)/(sqrt(3)/2)=-1/sqrt(3)=-1/3*sqrt(3). Hence, the equation y=-x*sqrt(3)/3 is the equation in rectangular coordinates.