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.

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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 .

Apply product rule of derivatives: .

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Find .

Consider .

Apply derivative on each side with respect to .

.

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Substitute and .

Slope of the parametric equation is .

Slope of the tangent line is .

Slope of the horizontal tangent line is .

and .

and .

and

and .

The solutions of on are .

Substitute in polar equation .

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Substitute in polar equation .

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Substitute in polar equation .

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

Slope of the vertical tangent line is .

and

and .

and .

Substitute in polar equation .

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Substitute in polar equation .

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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 tangent line is vertical are , and .