Have you tried finding the maximum point of i by differentiating it? Alternatively, you can convert sin(t) + cos(t) to just sine using these formulas.
This is a calculus subforum. One of the best-known facts in calculus is Fermat's theorem.
Also, I assume you know how to find the maximum of for some constants A and . The link in post #2 shows a formula for converting 2sin(t) + 2cos(t) into for some A and .
If this is not clear, please explain precisely what your difficulty is and what methods you know for finding maxima of functions.
So you have a problem like this and have never taken Calculus? That makes it a little harder but it can be done.
You know, I hope, that sin(a+ b)= cos(a)sin(b)+sin(a)cos(b). Taking b= x, you could use that immediately if you could have cos(a)= sin(a)= 2 but that is impossible because that would mean which, of course, can't be true because for all a.
But we can fix that: rewrite 2sin(x)+ 2cos(x) as . Now, we can say that because then as required.
So we can write
Now use the fact that cos(x) has a maximum value of 1.