# What is the slope of the tangent line of #r=thetacos(theta/4-(5pi)/3)# at #theta=(-5pi)/3#?

##### 1 Answer

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 :)