Can any function be written as a linear combination of only sines?

Question

In the fourier transform sines and cosines are used to form an orthogonal basis. But since $\sin x$, $\sin 2x$, $\sin3x$ are already orthogonal, why do we even need the cosine terms to represent a function? The same applies for cosines, why do we need sines? If $\sin nx$ form an orthogonal basis, can't any vector (in this case function) be represented as a linear combination of sines only?