Determine an equation of a cosine function, given the following info: Amplitude: 3 Period: 120 V.Shift: 6 The function has a maximum at 15?

1 Answer
Tony B
Mar 19, 2017

Finally sorted out! See the explanation.

Explanation:

The max/min ( amplitude) of #cos(x)# is +1 and -1. So if you wish to increase this to #color(red)(+-3)# we have #y=color(red)(3)cos(3(x-15))#

'Shifting' the graph to the right so that #ul(color(red)("a"))# maximum (not 'the' maximum) is achieved by looking at the plot of #cos(x)# at the point #color(red)(x-15)# and plotting it at #x#. Hence the #y=3cos(3(color(red)(x-15)))# The consequence is that the whole graph has been 'shifted' to the right by 15

'Squashing the curve is achieved by looking at a point for #color(red)(3)x " using "cos(x)# and plotting it at #x #. Hence the #y=3cos(color(red)(3)(x-15)) #

Tony B

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