# Thread: Decide the value of constant a

1. ## Decide the value of constant a

Hi!

I´m really mostly curios about how I can simplify after I differentiate.

$y = sin^2(ax) \ \mbox{is given}$

Decide the value of a if $\frac{dy}{dx} \ = 1 \ \mbox{when} \ x = \frac{\pi}{4}$

Is this differentiation correct? $\frac{dy}{dx} = 2a*sin(ax)*cos(ax)$ ?

Now, can I rewrite this using the trig.identity $2*sin(x)*cos(x) = sin (2x)$ ?

How would it look like in that case?

Thanks

2. Yes, you can write it as $asin(2ax)$

Then, $asin(\frac{{\pi}a}{2})=1$

3. ## hi

Thanks! Thats what I did!

Now, what values of a do you find giving us $\frac{dy}{dx} = 1$ ?

4. Newton's method is always an easy way to solve something like this.

2 values are -1 and 1

5. ## hi

thanks!

To be honest, I had already solved this for a =1 and a=-1

But my book which I am working from says only a = 1 , and I definetely thought it should be a = 1 and a = -1

Thanks very much for helping me confirm this galactus!

6. When we solve, actually, we get many solutions. But all may not be viable.

i.e. when I run it through my TI, I get solutions:

a = -33.981, -32.02, -1, 1, 1.5555, 4.1547, 89.993