# Thread: Graphs of sin and cos

1. ## Graphs of sin and cos

Hello I know the formula for a minimum point in a quadratic curve (-b/2a) but I've been faced with a graph of y=sinx and I need to find the coordinates of the maximum point.

I've gussed at 45,90. Any help?

2. Originally Posted by Mukilab
Hello I know the formula for a minimum point in a quadratic curve (-b/2a) but I've been faced with a graph of y=sinx and I need to find the coordinates of the maximum point.

I've gussed at 45,90. Any help?
Dear Mukilab,

A sinosoidal curve is an oscillating curve, hence having infinite number of maximum points. But if you consider a particular domain, such as $0\leq{x}\leq{\pi}$ you will be able to find some maximum points in that domain. Maximum points occur when,

$x=........-\frac{3\pi}{2},\frac{\pi}{2},\frac{5\pi}{2},\frac{ 9\pi}{2}..........$

Hence $x=\frac{n\pi}{2}~where~n=........-7,-3,1,5,9,13,........$

And since $-1\leq{\sin{x}}\leq{1}$ the maximum value of sinx is 1.

Therefore one could write the coodinates of the maximum points as, $\left(\frac{n\pi}{2},1\right)~when~n=.........,-7,-3,1,5,9,13..........$

Hope this will help you.

3. I'm sorry, I don't understand at "Maximum points occur when

Hence "

and"Therefore one could write the coodinates of the maximum points as, "

4. Originally Posted by Mukilab
I'm sorry, I don't understand at "Maximum points occur when

Hence "

and"Therefore one could write the coodinates of the maximum points as, "
Dear Mukilab,

Do you know that the maximum value of sinx is 1? And do you know that, sinx=1 when $x=\frac{\pi}{2}$?

5. Sorry for my rash answer, all those functions did my head in.

I've looked at quite a few interactive graph plotters since then and I understand this:

Take a and b as intergers
acos(bx)

a will make the minimum and maximum y points that interger (e.g. 3cos, max y=3, min=-3)

b will make the peaks closer together, roughly halving it (cos2x has y=0 on 45, cosx has y=0 on 90)

What I don't understand is how these interact.

Common logic says 3cos2x should have a point at y=0 with coordinates 45,0 and a minimum point with coordinates 90,-3

but its not true!

6. Originally Posted by Mukilab
What I don't understand is how these interact.

Common logic says 3cos2x should have a point at y=0 with coordinates 45,0 and a minimum point with coordinates 90,-3

but its not true!
It is true. $3\cos{2x}=0~when~x=\frac{\pi}{4}$ and $3\cos{2x}=-3~when~x=\frac{\pi}{2}$