Question

Find the slope of the tangent line to the given polar curve at the point specified by the value of θ.

r = 1/θ,       θ = π

Answer 1

Step 1:

The polar equation is .

If the point P  has cartesian coordinates and  polar coordinates , then

.

Substitute in polar coordinates.

.

 

Apply derivative on each side with respect to .

Apply derivative on each side with respect to .

Step 2:

Find .

.

Substitute and in above expression.

At the point .

Solution:

Slope of the tangent line is .