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

1 Answer
Dec 19, 2017

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

enter image source here

Hopefully this helps!