Question

If the sin(50) = 10/15 what is cosine(40)? Can someone explain this to me ...

Answer 1

Recall that

$\cos(90-x)^\circ=\sin x^\circ$

which tells you that $\cos40^\circ=\cos(90-50)^\circ=\sin50^\circ$, so in fact

$\cos40^\circ=\sin50^\circ=\dfrac{10}{15}$

Attached is an image demonstrating why the identity is true.