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

Problem

y=arctan(x)

Solution

1. Identify the function type. The function y=arctan(x) is an inverse trigonometric function, not a periodic sinusoidal function like sine or cosine.

2. Determine the amplitude. Amplitude is a property of periodic waves (the distance from the center to a peak). Since the arctangent function is not periodic and does not oscillate, the concept of amplitude does not apply.

3. Determine the period. A period is the interval after which a function repeats its values. The arctangent function is strictly increasing and does not repeat; therefore, it has no period.

4. Determine the phase shift. Phase shift refers to the horizontal displacement of a periodic function from its standard position. Because this function is not periodic, there is no phase shift.

Final Answer

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

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