I do not have any idea to deal with this question, can anyone help?

It is given that

,

where 0 <= x <= 2x.

If y has the maximum value when x =

and the minimum value when x = ,

find the values of and .

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- Apr 17th 2006, 08:08 AMling_c_0202FIND sin alpha and sin beta
I do not have any idea to deal with this question, can anyone help?

It is given that

,

where 0 <= x <= 2x.

If y has the maximum value when x =

and the minimum value when x = ,

find the values of and . - Apr 17th 2006, 09:01 AMThePerfectHackerQuote:

Originally Posted by**ling_c_0202**

The amplitude is 5, thus it max is 5. Max happens where is max. Sine is max when Thus, at .

Similary the minimum occurs at thus, - Apr 17th 2006, 09:17 AMling_c_0202
sorry

I typed the questioned wrongly.

It should be

It is given that y = sin x + 4 cos x,

where 0 < = x <= 2pi.

If y has the maximum value when x = alpha

and the minimum value when x = beta,

find the values of sin alpha and sin beta. - Apr 17th 2006, 10:34 AMThePerfectHackerQuote:

Originally Posted by**ling_c_0202**

, then, do the following trick,

Think, of a right triangle with legs then its hypotenuse is thus, if is an angle between the hypotenuse and then you have,

Thus, substituting that into our expression,

Thus, sum for sine of two angles,

where

------------------

Let us return back to your problem.

You have thus, using this trick you have,

where

As explained before the max occurs when,

Thus,

Thus,

Thus,

We need,

Which is,

----------------------------

For the min that happens when,

Thus,

Thus,

Thus,

But you need,

But,

Thus,