Question

Write the following function in the form Acos(ωt−δ).
x(t) = cos t + sin t

Answer 1

Use
\[
\sin(t)= \cos(\pi/2 -t)\\
\cos(u) + \cos(v)= 2 \cos(1/2(u+v) \cos(1/2(u-v)
\]

Answer 2

This will do it

Answer 3

Say we have
\[y=A \cos(t)+B \sin(t) \\ y=\sqrt{A^2+B^2}(\frac{A}{\sqrt{A^2+B^2}} \cos(t)+\frac{B}{\sqrt{A^2+B^2}} \sin(t) )\]

So then you have...
you should be able to finish it from here actually