Select the type of curve described by the polar equation tan θ = 2.

Circle
Ellipse
Line
Point
Spiral

Note that, since tanθ = sinθ/cosθ, we see that:
tanθ = 2
==> sinθ/cosθ = 2
==> sinθ = 2cosθ.

Then, multiplying both sides by r gives:
r*sinθ = 2r*cosθ.

Then, using the conversions x = r*cosθ and y = r*sinθ gives:
y = 2x, which is the equation of a line.

Therefore, tanθ = 2 is a line.

I hope this helps!

tan θ = 2
θ = atan(2), which is a constant.

when θ = constant and r is anything (not defined), it is a line at θ direction.
**when r = constant and θ = anything (not defined), it is a circle of r.

It's a line and here is why.

solve for theta

theta = tan^-1(2) now think of it this way: at any given theta(angle) you will always get the constant tan^-1(2).

it's much like y=2 for any given y value the x value will equal 2.