Increasing and Decreasing Functions (max/min)

[JOhnJDC]

Homework Statement

Find a > 0 so that the curves y = sin ax and y = cos ax intersect at right angles (let them intersect at (x0, y0)).


2. The attempt at a solution

Thinking about the unit circle, if theta equals pi/4, then sin theta and cos theta would intersect at right angles at the point (1/sqrt2, 0). Does this imply that sin ax0 = cos ax0? I don't know where to go from here. This problem is at the end of a section that concerned what I can learn about the graph of a function from the first derivative of the function. However, I don't see how the derivatives of the above functions can help me here. I would greatly appreciate a walk-through.

 

[Roni1985]

you know one thing if they intersect at right angle, the multiplication of their slope should be negative 1.
say
m1=3
m2=-1/3
that means that they are perpendicular

Now, what do derivatives give you ?

I'm not sure if this works, but you should try