# What is the period and amplitude for f(x)=3cos2x?

1] The number multiplying the $\cos$ represents the AMPLITUE. So your $\cos$ oscillates between $+ 3$ and $- 3$;
2] The number multiplying the $x$ in the argument allows you to evaluate the PERIOD as: $\left(p e r i o d\right) = \frac{2 \pi}{\textcolor{red}{2}} = \pi$. This means that your function needs the length $\pi$ to complete one oscillation. graph{3cos(2x) [-10, 10, -5, 5]}