What is the slope of the tangent line of #r=thetacos(theta/4-(5pi)/3)# at #theta=(-5pi)/3#?
Find the change in radius with respect to theta,
Now, use the chain rule to derive a formula for gradient in polar coordinates:
We know the transformations for polar coordinates,
now, let's find the values for r', r and theta at your point.
Theta is defined to be
And now to find r',
We already evaluated the first cosine expression in the last, so I will just skip through a couple of things
Sorry, I don't have enough time to do the rest of it, but I think you can easily plug those values into the gradient formula derived and get your answer :)