Question

How do you graph `y= 6 sin x`?

Answer 1

The same shape as sin(x) but the amplitude is 6 times bigger.
`sin(x) " max" = +-1 " whilst " 6sin(x) "max"=+-6`

Explanation:

If y= something then `6 times "something"` is also going to make y 6 times bigger.

The curve repeats every `360^0` which is `2pi` radians.
The measure of its repeat is called its pitch. Notice that it crosses the origin. The cos curve is the same shape and amplitude but it is shifted "transposed" to the right by `90^0` which is `pi/2` radians. The curve crosses the x-axis every `180^0` or `pi/2` radians. This is 1/2 the pitch.