Find Amplitude, Period, and Phase Shift y=arccos(x)

Problem

y=arccos(x)

Solution

1. Identify the function type. The function y=arccos(x) is an inverse trigonometric function, not a periodic sinusoidal function like sin(x) or cos(x)

2. Determine the amplitude. Amplitude is a property of periodic waves representing the distance from the center to a peak. Since y=arccos(x) is not periodic, the amplitude is undefined.

3. Determine the period. The period is the interval after which a function repeats its values. Since y=arccos(x) is a strictly decreasing function on its domain [−1,1] and does not repeat, the period is undefined.

4. Determine the phase shift. Phase shift refers to the horizontal displacement of a periodic function. Because this function is not periodic, the concept of phase shift does not apply.

Final Answer

Amplitude: None, Period: None, Phase Shift: None

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