I am having trouble solving this problem:

"Find where the tangent line is horizontal for r=1+cos(theta)"

I would really appreciate the feedback, I'd like to know how to go about solving problems like these. Thank you!

Where the derivative is zero

dr/dT = - sin T
so when T = 0 or n * pi

To find where the tangent line is horizontal for the polar equation r = 1 + cos(theta), we need to determine the values of theta where the derivative of r with respect to theta (dr/dtheta) equals zero.

Here's how you can go about solving this problem:

1. Start by finding the derivative of r with respect to theta. Since r is defined in terms of theta, you'll need to use the chain rule. By doing the calculations, you'll find that dr/dtheta = -sin(theta).

2. Set the derivative equal to zero and solve for theta:
-sin(theta) = 0

3. To find the values of theta that satisfy this equation, we need to determine when sin(theta) = 0. The values where sin(theta) equals zero are at theta = 0, pi, 2pi, 3pi, etc.

4. Therefore, the tangent line is horizontal at those values of theta where r = 1 + cos(theta), when theta = 0, pi, 2pi, 3pi, etc.

To summarize, the tangent line is horizontal for the polar equation r = 1 + cos(theta) at the values of theta where theta = 0, pi, 2pi, 3pi, etc.