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

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 $\frac{2 \pi}{b}$, where $b$ is the $\sin \left(b x\right)$. Therefore, the period is $\frac{2 \pi}{6} = \frac{\pi}{3}$. 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!