Question

What is the equation of the sinusoid shown in the graph?

A. y=3cos(pi/2x)
B. y=3cos(4x)
C. y=cos(4x)
D. y=3cos(1/4x)

Answer 1

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Explanation:

Answer 2

Answer: C

Explanation:

The Cosine Function

The graph of a cosine function is a sinusoid that starts at its maximum value of 1 at x=0 and takes x=2π radians to complete a full cycle. The function of the parent cosine function is:

`y=\cos x`

Both the amplitude A and the angular frequency w of a cosine can be modeled by the function

`y=A\cos(\omega x)`

The graph of the cosine function shown in the figure has an amplitude of A=3 and it completes a full cycle at x=π/2, thus:

`(\pi)/(2)\omega =2\pi`

Thus:

`\omega = 4`

Therefore, the equation of the sinusoid is:

`y=3\cos (4x)`

Answer: C