determine sine minimum and maximum within an interval

**Zestje** · 04-23-2015, 03:32 PM

Hello,

I'm trying to determine the minimum and maximum value of the sine function within a set interval. I can't find an easy way to do this so I'm asking here for help.

The two input values are variable and lie within the range of -90º to + 450º. It's easy to determine the value of the sine function for the start and end of the interval, e.g. sin(-35) and sin(276), but how do I determine if there is an absolute maximum (with value 1) or absolute minimum (with value -1) within that range?
I would then implement a check to determine the maximum and the minimum values of those at maximum 4 different values.
If possible I prefer not to have a VBA solution, but if it's easier or better that would still be OK.

Any help is appreciated!

**MrShorty** · 04-23-2015, 04:08 PM

Since you know that the absolute maximum value for the sine function occurs at 90° (pi/2 radians), then you could simply test for minimum angle<=90<= maximum angle. Similar for the absolute minimum of the sine function. If your defined angle intervals does not include these two points, then you need only evaluate the sine function at the endpoints of the interval and determine which is max and which is min for that interval.

If you wanted to, you might consider a generic numeric approach. In Excel, this might be easiest using the Solver add-in. Enter the sine function and the interval in a spreadsheet. Then set up the Solver model to maximize (or minimize) the cell with the sine function by changing the angle subject to constraints that the angle is between the defined angles.

**Zestje** · 04-24-2015, 06:34 AM

That's exactly what I needed to know!

I was testing and analysing the separate intervals between peaks intead of just testing for the peaks themselves, which is a lot easier! I was so close and just didn't think of it...