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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.$$y=1-\cos \left(2 x-\frac{\pi}{3}\right)$$

$\pi / 6$

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Heather Z.

Oregon State University

Kayleah T.

Harvey Mudd College

Caleb E.

Baylor University

Michael J.

Idaho State University

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Video Transcript

so we have. Why is equal to one minus co. Sign off two X minus height over sea, and this can be figured in as y school to one minus co. Sign off two times X minus pi over six. So the altitude ISS won. The period is two pi over two, which is equal to pi. And there's a phase shift equal to pi over six. And there's also a word of The shift is equal to one, and there's only one X intercept, and Juan X X intercept is at X is equal to high or six. And then on the graph, you can see the location off the maximum point the quarters to power three, comma two and in accordance off the minimum point rpai or six comma zero.

Other Schools
Heather Z.

Oregon State University

Kayleah T.

Harvey Mudd College

Caleb E.

Baylor University

Michael J.

Idaho State University