Questions: Determine the amplitude, period, and phase shift of the following trigonometric equation. y=-1/3 cos(x-5)

Determine the amplitude, period, and phase shift of the following trigonometric equation. y=-1/3 cos(x-5)
Transcript text: Determine the amplitude, period, and phase shift of the following trigonometric equation. \[ y=\frac{-1}{3} \cos (x-5) \]
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Solution

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Solution Steps

Step 1: Identify the Function Type

The function is of type cos.

Step 2: Extract Parameters

The given parameters are A = -0.333, B = 1, C = -5, and D = 0.

Step 3: Calculate Amplitude

The amplitude of the function is |A| = 0.333.

Step 4: Calculate Period

The period of the function is \(\frac{2\pi}{|B|} = 6.28\).

Step 5: Calculate Phase Shift

The phase shift of the function is \(-\frac{C}{B} = 5\).

Step 6: Determine Vertical Displacement

The vertical displacement of the function is D = 0.

Step 7: Adjust for Negative Amplitude

A negative amplitude indicates a reflection over the x-axis. This affects the phase shift and should be considered when interpreting the function's graph.

Final Answer:

The function \(y = -0.333 cos(Bx + C) + D\) has an amplitude of 0.33, a period of 6.28, a phase shift of 5, and a vertical displacement of 0.

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