How do we get negative values in this graph?

Question

Why does the following function have negative values?
E.g for x = 0.8 the value of y is negative but neither sin(0.8 * 6) is negative nor the 3^(-x/3).

Answer 1

You seem to be thinking of $\sin(4.8)$ as the sine of $4.8°$, where a full circle corresponds to $360°$. This is not how this function is defined in mathematics, and it is not what was meant in the graph. The usual definition is that we measure the angles in such a way that a full circle corresponds to $2\pi$, which is the length of the unit circle. (This is why this is called arc length.)