Question

How do you find the period, amplitude and sketch `y=-2sin6x`?

Answer 1

Amplitude is `2`, or the coefficient in front of the sine. Amplitude is the vertical distance between a maximum/minimum and the centre axis of the graph.

The period is always given by `(2pi)/b`, where `b` is the `sin(bx)`. Therefore, the period is `(2pi)/6 = pi/3`. The period is how many radians it takes the graph to repeat itself.

The graph has endured a reflection over the y-axis, because the leading coefficient, or `a` term, is negative.

When graphing, remember that sinusoidal functions are cyclic, or they repeat to infinity. The shape isn't a straight line, so there should always be a curve, and you pencil should never leave the page when drawing them.

In the end, you should get the following graph

Hopefully this helps!