Year 12 further maths help!

I'm really struggling with this 2018 WJEC paper 😭 and it's due tommorow

which one / what have you tried?

4 - I've differentiated to get the velocity but I have no idea how to try to get the value of t let alone the rest of the question

If its (instantaneously) at rest, then each component must be zero, which is just working out when a few trig terms are simultaneously zero? The momentum part should be straightfoward as should the force (acceleration/rate of change of momentum)?

I'm not going to lie - what you just said went right over my head. So could you just make cos(t) 0? And then mess round with the sine to get the answer?

You have something like
v(t) = cos(t) i + sin(2t) j + cos(t) k
so you want each of the i, j, k coefficients to be zero so
cos(t) = 0
sin(2t) = 0
cos(t) = 0
A simple sketch of the trig functions or when is cos(t) = 0 and which of those solutions correspond to sin(2t) = 0.

Thank you! I think I got it

Looks about right. Minor quibble (which you should have come across) is when you say
cos^(-1)(0) = pi/2
in this case youre lucky as the first value also gives sin(2t) = 0. More generally it would be better to write something like
cos(t) = 0
t = pi/2 + k*pi
so explicitly write out all the possible solutions for cos, then verify which is the first one that satisfies sin(2t)=0, so k=0.
If you just want to refer to the principal solution, it would be better to say
arccos(0) = pi/2
as arccos is the inverse of cos on the restricted domain 0 to pi.
Also, you can get force by differentiating momentum (as youve already stated that). Theres no need to go back to velocity and then multiply by mass.

Would anyone know how to do this either? I don't understand how to reduce the top from that to something more understandable

If youre asked for partial fractions, then that requires the original fraction is proper. Do you know what that means, What to do it first?