The graph below is one complete cycle of the graph of an equation containing a trigonometric function. Find an equation to match the graph. If you are using a graphing calculator, graph your equation to verify that it is correct.

B)
C)
D)

Question

The graph below is one complete cycle of the graph of an equation containing a trigonometric function. Find an equation to match the graph. If you are using a graphing calculator, graph your equation to verify that it is correct. ​
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B)​ 
C)​ 
D)​

Quizplus · Accepted Answer

The graph starts at its maximum point, so we know the function must be of the form $f(x)=a\cos(bx)+c$. The maximum value of the graph is 3, so $a=3$. The graph completes one cycle over the interval $0\leq x\leq 2\pi$, so we can set $b=2\pi$. Finally, we can see that the graph has a minimum value of -3, so $c=-3$. Therefore, the equation for the graph is $f(x)=3\cos(2\pi x)-3$, which matches choice B.

The Graph Below Is One Complete Cycle of the Graph