# How do you graph y=sin(3x) over 0<=x<=540?

Jan 11, 2017

See the graph and the explanation.

#### Explanation:

${540}^{o} = 3 \pi$ radian = 9.425 units of distance, on the x-scale.

The period of $\sin \left(3 x\right) = \frac{2 \pi}{3}$.

So, the specified interval is 4.5 periods long.

The amplitude of the wave is 1,

So, the the number of the given sine waves, in this period is 4.5.

I have given two graphs. In the second, $y \in \left[- 1 , 1\right]$ to reveal the

amplitude, in exactitude. See the gaps at the crests and nadirs.

To close that, the y-interval is increased a bit, for the first graph.

The gaps in the second are magnified ( empty ) point gaps that are

interpreted as turning points..

graph{sin (3x) [0, 9.425, -1.1, 1.1 ]}

graph{sin (3x) [0, 9.425, -1, 1 ]}