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# Determine the amplitude, period, and phase shift for the given function. Graph the function over one period. Indicate the $x$ -intercepts and the coordinates of the highest and Iowest points on the graph.$$y=3 \cos \left(\frac{2 x}{3}+\frac{\pi}{6}\right)$$

## $-\pi / 4$

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##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

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### Video Transcript

so we have this equation. Why is equal to three co sign off to over three x plus pi over six? This can be rewritten as why is equal to three times co sign off to over three x plus one up i over four. The aptitude is equal to three. The P AED is two pi divided by 2/3, which is equal to de pie and then the face shift is equal to negative pipe. Over four. There are two X intercepts at X is equal to high over to and at X is equal to two pi, and you can get the corners off the maximum point from the graph, and you can also get the quarters off the minimum point from the graph.

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##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor