# PreCalculus/Trigonometry graphing and equations?

Write the positive sine y = d + asin(bx - c) and cosine y = d + acos(bx - c) functions for the graph.

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- 1 month agoFavourite answer
Period is 4pi/8, or pi/2

Amplitude is 2

Axis of symmetry is y = 0

y = 0 + 2 * sin(bx - c)

y = 2 * sin(bx - c)

No horizontal shift here. c = 0

y = 2 * sin(bx)

b = 1, then period is 2pi

b = 2, then period is pi

so

period is 2pi / b

2pi / (pi/2) =>

4

y = 2 * sin(4x)

Guess what? It'll be mostly the same for cosine as well. It'll just be shifted

y = 2 * cos(4x - c) + 0

y = 2 * cos(4x - c)

It's shifted pi/8 units to the right. But we have to do something first. We have to rewrite this as:

y = 2 * cos(4 * (x - c))

Where c is our shift to the right.

4 * pi/8 = pi/2

y = 2 * cos(4x - pi/2)

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