1. ## Finding Largest Magnitude

Suppose that at any given time t (in second) the current i (in amperes) in an alternation current circuit is i=2cost+2sint
What is the peak current for this circuit. ( The largest magnitude)

2. ## Re: Finding Largest Magnitude

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.

3. ## Re: Finding Largest Magnitude

I'm sorry that did not help me at all

4. ## Re: Finding Largest Magnitude

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 $A\sin(t+\varphi)$ for some constants A and $\varphi$. The link in post #2 shows a formula for converting 2sin(t) + 2cos(t) into $Asin(t+\varphi)$ for some A and $\varphi$.

If this is not clear, please explain precisely what your difficulty is and what methods you know for finding maxima of functions.

5. ## Re: Finding Largest Magnitude

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 $cos^2(a)+ sin^2(a)= 4+ 4= 8$ which, of course, can't be true because $cos^2(a)+ sin^2(a)= 1$ for all a.

But we can fix that: rewrite 2sin(x)+ 2cos(x) as $2\sqrt{2}(1/(\sqrt{2})cos(x)+ 1/(\sqrt{3})sin(x))$. Now, we can say that $cos(a)= sin(a)= 1/(\sqrt{2})$ because then $sin^2(a)+ cos^2(a)= 1/2+ 1/2= 1$ as required.

So we can write
$2sin(x)+ 2cos(x)= 2\sqrt{2}(1/\sqrt{2}cos(x)+ 1/\sqrt{2}sin(x))$
$= 2\sqrt{2}(sin(\pi/4)cos(x)+ cos(\pi/4)sin(x))= 2\sqrt{2}sin(x+ \pi/4)$.

Now use the fact that cos(x) has a maximum value of 1.

6. ## Re: Finding Largest Magnitude

Originally Posted by HallsofIvy
you could use that immediately if you could have cos(a)= sin(a)= 2 but that is impossible
My ROTC officer used to say that in wartime, the value of sine can reach 2, and by the order of the commander-in-chief, even 4