Question

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

Answer 1

Draw the sine wave for the equation f(x) = 5 sin (x + `alpha`), where `sin alpha = 4/5 and cos alpha = 3/5`. The is the graph. It is periodic, with period `2pi`, The amplitude of the wave is 5.

Explanation:

With the notations, in the answer, `f(x) = 5 (sin x cos alpha + cos x sin alpha ) = 5 sin (x+alpha)`.
This is the equation for the sine wave with period `2pi` and amplitude 5
the graph cuts the f-axis at (0, 5 sin `alpha`)..