Periodic functions > Trigonometric graphs and equations
123456Trigonometric graphs and equations

Theory

Take a look at the applet

The graph of the function g ( x ) = a sin ( b ( x + c ) ) + d is a sinusoid. That is a graph that results when you transform the graph of a standard sine function f ( x ) = sin ( x ) . The graph of g has the following properties:

  • the amplitude (maximum deviation from the equilibrium) is a ;

  • the period is 2 π b so b = 2 π period ;

  • the horizontal translation is - c ;

  • the equilibrium is the line y = d .

Take a look at the following applet:

The graph of the function g ( x ) = a cos ( b ( x + c ) ) + d is a sinusoid. That is a graph that results when you transform the graph of a standard cosine function f ( x ) = cos ( x ) . The graph of g has the following properties :

  • the amplitude ( maximum deviation from the equilibrium ) is a ;

  • the period is 2 π b so b = 2 π period ;

  • the horizontal translation is - c ;

  • the equilibrium is the line y = d .

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