Define the period of a trigonometric graph. Sketch f(x) = x and h(x) = 2 x for $0^ x 360^", classify their amplitudes and ranges.

3.3.1 The period of a trigonometric graph is the length of one complete cycle before the graph starts to repeat itself.

3.3.2 To draw the graphs of $f(x) = \cos x$ and $h(x) = 2\sin x$ on the same set of axes for $0^\circ \le x \le 360^\circ$:

• Set up axes: Draw an x-axis labeled from $0^\circ$ to $360^\circ$ (with markings at $90^\circ, 180^\circ, 270^\circ$) and a y-axis labeled from $-2$ to 2.
• Graph $f(x) = \cos x$ (standard cosine wave):
  • Plot points: $(0^\circ, 1)$, $(90^\circ, 0)$, $(180^\circ, -1)$, $(270^\circ, 0)$, $(360^\circ, 1)$.
  • Draw a smooth curve connecting these points.
• Graph $h(x) = 2\sin x$ (sine wave with amplitude 2):
  • Plot points: $(0^\circ, 0)$, $(90^\circ, 2)$, $(180^\circ, 0)$, $(270^\circ, -2)$, $(360^\circ, 0)$.
  • Draw a smooth curve connecting these points.
  • Label each graph clearly, e.g., "$f(x) = \cos x$" and "$h(x) = 2\sin x$".

3.3.3 The amplitude of $f(x) = \cos x$ is the absolute value of the coefficient of $\cos x$.
For $f(x) = 1 \cdot \cos x$, the amplitude is $|1|$.
The amplitude of $f(x)$ is $\boxed{1}$.

3.3.4 The range of $h(x) = 2\sin x$ is determined by its amplitude. The general form $A\sin x$ has a range of $[-A, A]$.
For $h(x) = 2\sin x$, the amplitude is 2.
The range of $h(x)$ is $\boxed{[-2, 2]}$ or $\boxed{-2 \le y \le 2}$.