Algebra 2 Will give medal

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Algebra 2 Will give medal

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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Remember \[\large acos(bx)+d\]\[\large amplitude~=~a\]\[\large period~=~\frac{2\pi}{b}\]\[\large Vertical~change~=~d\] If the maximum is 4 and the minimum is -2, the distance between them is 6. Half of 6 is 3, so the amplitude would be 3. Since the midline is usually 0 for the cos function, with no vertical change, the maximum and minimum would be 3 and -3 respectively. To boost them both up by 1, we'd make the vertical change +1. Finally the period is \(\large \frac{\pi}{2}\) so we can make the formula \[\large \frac{\pi}{2}~=~\frac{2\pi}{b}\] in order to find out what b is.
to get the phase shift we take (4x+pi)=0 and slove for x so 4x=-pi x=-pi/4 the period i pi in the tan function, so pi/4

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