# How do you use transformation to graph the cosine function and determine the amplitude and period of y=-4cos(-3x)?

May 29, 2017

As cosine is an even function we have that $\cos \left(- x\right) = \cos x$

so, $\cos \left(- 3 x\right) = \cos \left(3 x\right)$

Hence, $y = - 4 \cos \left(- 3 x\right) = - 4 \cos \left(3 x\right)$

If we start with the graph of $y = \cos x$, we need to apply a horizontal squash factor of $\frac{1}{3}$ to get $y = \cos \left(3 x\right)$

i.e. the period changes from 360 degrees to 120 degrees

From $y = \cos \left(3 x\right) \to y = - 4 \cos \left(3 x\right)$ we apply a stretch factor of 4 parallel to the y-axis and reflect about the x-axis due to the -4

The amplitude is 4.

See the graph below:

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