How do transformations affect the graph of y = sin (x) and y= cos(x)?

The general form for a sine function is

y = A*sin(B(x-C)) + D

where,

Put another way,

For example,

y = 3sin(2(x-5)) + 10

has

The same basic idea applies to cosine graphs as well because cosine is a cofunction of sine.

  The same way they affect the graphs of any other functions.

Step-by-step explanation:

The transformations we're generally concerned with are ones that re-scale the graph vertically or horizontally, or shift it vertically or horizontally. Such transformations have the same effects on any function.

The given functions are periodic, so certain reflections and horizontal translations will appear to have no effect. For example, the functions ...

  y = sin(x)

  y = sin(x +2π)

will have identical graphs. (That is the meaning of "has a period of 2π". A horizontal shift by any multiple of the period gives the same graph.)

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