proof of cosx and sinx are orthogonal?

[krumpli]

proof of cosx and sinx are orthogonal?

i couldnt find any proofs by googling -_- thank you for your further helps

 

[pka]

proof of cosx and sinx are orthogonal?
i couldnt find any proofs by googling

That does not surprise me at all.
I cannot think of any context in which the terms $\displaystyle \sin(x),~\cos(x)$ and orthogonal have any relationship.
I do suspect there is a translation problem here.

 

[daon2]

In terms of the vector space $\displaystyle \mathcal{C}[-L,L]$, they are orthogonal with respect to the inner product

$\displaystyle \displaystyle \left\langle \sin\left(\dfrac{m\pi x}{L}\right), \cos\left(\dfrac{n\pi x}{L}\right)\right\rangle = \int_{-L}^L \sin\left(\dfrac{m\pi x}{L}\right)\cos\left(\dfrac{n\pi x}{L}\right) dx$

This inner product is used in Fourier analysis. See here for more specifics. Both are also orthogonal to the span of the vector $\displaystyle f(x)\equiv 1$.

edit: Or maybe, OP is being asked to show sin(x) and cos(x) intersect at right-angles. To prove this, show that their derivatives at intersection points differ by a factor of -1. Then conclude their tangent lines are orthogonal.