What is the difference between the graph of f ( x ) = sin ( 4 x ) and that of f ( x ) = sin ( 5 x ) cos x - cos ( 5 x ) sin x ?

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What is the difference between the graph of             f              (        x        )              =          sin              (        4        x        )             and that of             f              (        x        )              =          sin              (        5        x        )                    cos      x        -          cos              (        5        x        )                    sin      x      ?

Nathanael Bates · Accepted Answer

Graph of             f              (        x        )              =          sin              (        4        x        )             is as follows: graph{sin(4x) [-5, 5, -2.46, 2.54]}Graph of             g              (        x        )              =          sin              (        5        x        )                    cos      x        -          cos              (        5        x        )                    sin      x       is as follows: graph{sin(5x)cosx-cos(5x)sinx [-5, 5, -2.46, 2.54]}The similarity between the two is obvious. The reason is that             sin              (        4        x        )              =          sin              (        5        x        )                    cos      x        -          cos              (        5        x        )                    sin      x      This is as             sin              (        A        -        B        )              =          sin      A              cos      B        -          cos      B              sin      A       and putting       A    =    5    x   and       B    =    x   we get above result.

What is the difference between the graph of f ( x ) = sin (...

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