Find the range of .

Ideas?

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- January 2nd 2011, 02:59 PMatreyyuRange of trig function
Find the range of .

Ideas? - January 2nd 2011, 03:03 PMdwsmith
What do you know about sine?

- January 2nd 2011, 03:14 PMatreyyu
Well, enough to know that even though the range of sine is <-1;1>, the range of f will not be ...

What else would be any help? - January 2nd 2011, 03:18 PMdwsmith
- January 2nd 2011, 03:33 PMdwsmith

If , then .

What is the max value this can be?

Once you determine the x value that obtains the max, x_0, of , then

The question then remains is - January 2nd 2011, 03:37 PMmr fantastic
- January 2nd 2011, 07:29 PMSammyS
It's clear that f(x) has a minimum value of zero; at x=0 for instance.

and

Then,

At this point we have that:

A not so well known trig identity gives:

We now have:

Now use a product to sum identity on:

Finally,

I suggest finding the minimum and maximum values of the expression inside the brackets. Square those then divide by 2.