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Problem 28 Medium Difficulty

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

Answer

$\pi / 2$

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Top Algebra Educators
GH
Grace H.

Numerade Educator

Heather Z.

Oregon State University

Kayleah T.

Harvey Mudd College

Kristen K.

University of Michigan - Ann Arbor

Video Transcript

so we have t equation. Why is equal to one over to sign times Pi X over two minus pi square, and this can be rewritten as wise. Quito one over to sign by over two times X minus two pi. So from here we see that the amplitude is 1/2. The p it is to pipe divided by pi over two. Which is he put before and then the phase shift is two pi. Okay, and you can see that the X intercepts there are two. So there's one text intercept us at Texas equal to 0.283 And then there's another one act exit. Go to 2.283 and the coordinates often maximum point are 2.3 point 283 0.5 and the coordinates off the minimum point of 1.83 point. Common Negative 0.5

Other Schools
Top Algebra Educators
GH
Grace H.

Numerade Educator

Heather Z.

Oregon State University

Kayleah T.

Harvey Mudd College

Kristen K.

University of Michigan - Ann Arbor