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.