# Sin wave Maximun/minimum finding?

1. Oct 29, 2008

### pjunky

For different values of x in positive increasing order,sin wave would be either
Max or Min, so I plotted all points.how to find out whether wave is max or min
at a given particular point from X.
Thanks.

Last edited: Oct 29, 2008
2. Oct 29, 2008

### Office_Shredder

Staff Emeritus
Can you describe the problem a bit better? It sounds like you have a sequence of values and some sort of sine function (Asin(w*t+b) as a function of t, A, b and w unknown) and want to know if you've hit a maximum. If that's what you're looking for, you can't do it

3. Oct 29, 2008

### Desh627

Well if you're thinking in terms of calculus, you don't need to graph this.

A function will have a relative maximum or minimum when its derivative is equal to zero (or at the endpoints of a piece of the function you're observing), and you can determine whether its a maximum or minimum by finding when its second derivative is equal to zero. When the second derivative is positive, the graph is concave up, and vice versa. A local maximum happens when you have the first derivative set to zero and the second derivative is negative. A local minimum happens when the first derivative is set to zero and the second derivative is positive. Beware, though, this is a general rule of thumb; there can be instances where the graph does not change concavity, or when a local minimum or maximum can be at the endpoint of such a piece of a function that you're looking at.

4. Oct 30, 2008

### pjunky

for Sin(0) wave is minimum,
for Sin(90) wave is maximum,
total:1,2,3,4,5,6,7........n-3,n-2,n-1,n
for Example assume at
1------->Max at x=1 ,y is max
2-------->Min at x=2,y is min
3------->Max
4------->min
5------->min
6------->min
.
.
.
n-1----->max at x=n-1,y is max
n------->min at x=n ,y is min

with out knowing y value,just with the help of 1,2,3,4...n how to know at a 3 or 4 or n-1
Y is max or min.

I got this clues,finding the 'area' bounded by the curve and with provided 1,2,3
finding out y is max or min at asked point.

Thanks.

Last edited: Oct 30, 2008
5. Oct 30, 2008

### pjunky

More clearly it would be like this

x=1,2,3,4,5,6,............n-2,n-1,n
for example
at x=1 sine wave is Maximum
at x=2 sine wave is Maximum
at x=3 sine wave is Min
at x=4 sine wave is Min
at x=5 sine wave is Maximum
at x=6 sine wave is Min
at x=7 sine wave is Maximum
at x=8 sine wave is Min
at x=9 sine wave is Min
at x=10 sine wave is Min
.
.
.
.
at x=n-1 sine wave is Min
at x=n sine wave is Max.

----------------------------------------------------------------
I mapped all the points,
so for x=1,how to find out wave is Max or Min
with out knowledge of wave.

----------------------------------------------------------------
I'm thinking like this finding out area bounded
by curve,and x values are given,so with the help
of 'area' and x values,I think I can find out y values(Max or Min)

Thanks.:surprised

6. Oct 30, 2008

### Office_Shredder

Staff Emeritus
If sin(1) and sin(2) are maxima, then sin(n) is a maximum for all n, as 1 is necessarily a period. I'm not sure what you're trying to get at

7. Oct 30, 2008

### pjunky

not like that you are taking sin(1),sin(2)...sin(n) as max

Just imagine x values in I quadrant in the graph.
now y values i.e sin wave values are mapped as min or max.

now have to find out at x=3 wave is max or min with out reading the wave.