what is dh/dt?

Differentiate h with respect to t. Sorry, have you learnt calculus yet?

Ah, you should be using the result from the first part to do the question, let me change my answer.

Part i is the clue for part ii. Essentially, finding the minimum of 3cos(t) - 5sin(t) is the same as finding the minimum of Rcos(t + a) for whatever a we discovered earlier. This can be done by making Rcos(t + a) = -R, which can be solved easily.

oh okay thank you

how do find the coordinates then?

Rcos(t + a) = -R
Means that t+a=pi, since cos(pi)=-1
So we have found t.
h would then be -R

so (t,-R) are the coordinates?

Yep

oh okay thank you