# When given a function of the form : y = acos[ b (pi - c)] + d, answer the following question: 1) When given a trigonometric word problem where a and b can be determined, how is the phase shift (c)...

When given a function of the form : y = acos[ b (pi - c)] + d, answer the following question:

1) When given a trigonometric word problem where a and b can be determined, how is the phase shift (c) and vertical shift (d) calculated?

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### 1 Answer

(1) The easiest way to compute the vertical shift is to take the average of the maximum and minimum. (If K is the max and L the min, we can find a by `(k-l)/2` and we can find d by `(k+l)/2` ). If you are given a graph you can also identify the maximum and minimum.

(2) To compute the phase shift you need to know a point. It is easiest if you know a maximum or a minimum. Since the cosine starts at a maximum (or a minimum if it is inverted) you know how far from the origin the function is starting.

** Note that there are an infinite number of possible values for c: once you find one, any number that is a multiple of the period from that point will work. For instance, if c=3 and the period is 5, then you can use -2,3,8,13,... as phase shifts. Usually you choose the smallest (in absolute value.)