Question

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

Answer 1

See the graph and the explanation.

Explanation:

`540^o=3pi` radian = 9.425 units of distance, on the x-scale.

The period of `sin (3x) = (2pi)/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 [-1, 1]` 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 ]}