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 $\displaystyle 0\leq{x}\leq{\pi}$ you will be able to find some maximum points in that domain. Maximum points occur when,
$\displaystyle x=........-\frac{3\pi}{2},\frac{\pi}{2},\frac{5\pi}{2},\frac{ 9\pi}{2}..........$
Hence $\displaystyle x=\frac{n\pi}{2}~where~n=........-7,-3,1,5,9,13,........$
And since $\displaystyle -1\leq{\sin{x}}\leq{1}$ the maximum value of sinx is 1.
Therefore one could write the coodinates of the maximum points as, $\displaystyle \left(\frac{n\pi}{2},1\right)~when~n=.........,-7,-3,1,5,9,13..........$
Hope this will help you.
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!