Slopes of tangent lines Find the slope of the line tangent to the following polar curves at the given points. At the points where the curve intersects the origin (when this occurs), find the equation of the tangent line in polar coordinates.

r = 4 cos θ;

Solution 6E

Step 1:

In this problem we have to find the slope of the line tangent to the curve at the point and we have to find the points where the curve intersects the origin.

We know that the slope of the curve at the given point is

We have

Therefore

Step 2:

Now