The polar equation is .

Find the points on the curve where the tangent line is horizontal or vertical.

Slope of the horizontal tangent line is .

Slope of the vertical tangent line is .

Find the slope of the curve.

If the point  has Cartesian coordinates  and  polar coordinates , then  and .

Substitute in polar coordinates.

.

.

The slope of the tangent line is derivative of the function.

Apply chain rule of derivatives : .

First find . 

Consider .

Apply derivative on each side with respect to .

.

Find . 

Consider .

Apply derivative on each side with respect to .

Apply product rule of derivatives: . \ \

.

.

Substitute and .

Slope of the parametric equation is

.

Slope of the tangent line is .

Slope of the horizontal tangent line is .

The general solution of  is .

If  then .

If  then .

Substitute in polar equation .

.

Substitute in polar equation .

The points on the curve where tangent line is horizontal are  and .

Slope of the vertical tangent line is .

The general solution of  is .

If  then .

If  then .

Substitute  in polar equation .

Substitute in polar equation .

The points on the curve where tangent line is vertical are  and .

The points on the curve where tangent line is horizontal are and .

The points on the curve where the tangent line is vertical are and .