Question

In exercises 41 and 42, find the slope of the tangent line to the polar curve at the given point.

r = 1 − sin θ at θ = 0

Answer 1

Given that

Now we have to find slope of the tangent line at

The slope of a tangent line to the curve is given by the general form

In the case of polar coordinates, we know that

We know that

Since, we get

Let us start by finding

Now, evaluate

Substitute the values in

Replace with 0.

The slope of the curve at is -1.