# How do you graph f(x) = 3 Sin x + 4 Cos x?

Draw the sine wave for the equation f(x) = 5 sin (x + $\alpha$), where $\sin \alpha = \frac{4}{5} \mathmr{and} \cos \alpha = \frac{3}{5}$. The is the graph. It is periodic, with period $2 \pi$, The amplitude of the wave is 5.
With the notations, in the answer, $f \left(x\right) = 5 \left(\sin x \cos \alpha + \cos x \sin \alpha\right) = 5 \sin \left(x + \alpha\right)$.
This is the equation for the sine wave with period $2 \pi$ and amplitude 5
the graph cuts the f-axis at (0, 5 sin $\alpha$)..