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y=5cos 4x
Graphs of sine and cosine functions are called sinusoids. Consider the general forms of transformed sine and cosine functions. Sine Function:& y= asin b(x- h)+ k Cosine Function:& y= acos b(x- h)+ k In these functions | a| is the amplitude, 2Ď€ b is the period ( b>0), h is the horizontal shift, and k is the vertical shift. One method to write a sine or cosine function that models a sinusoid is to find these values. Let's now consider the given graph.
To write a function for this sinusoid, we will follow four steps.
From the graph, we can see that the maximum value is 5 and the minimum value is - 5.
We can see that the graph crosses the y-axis at y=5.
Because the function passes through the y-axis at its maximum point, the graph is a cosine curve with no horizontal shift. This means that h= 0.
The shortest repeating portion of a sinusoid is called a cycle. The horizontal length of each cycle is called its period. Let's find the period of the given graph.
LHS * b=RHS* b
LHS * 2/Ď€=RHS* 2/Ď€
Ď€ * a/Ď€= a
Multiply
Because of the location of the graph's intersection with the y-axis, we concluded that the sinusoid shown should be modeled by a cosine function. We also found that a= 5, b= 4, h= 0, and k= 0. Finally, we can write the function. y= 5cos 4(x- 0)+ 0 ⇕ y=5cos 4x