Find Amplitude, Period, and Phase Shift y=tan((3x)/5)

Problem

y=tan((3*x)/5)

Solution

1. Identify the general form of the tangent function y=A*tan(B*(x−C))+D In this expression, A=1 B=3/5 C=0 and D=0

2. Determine the amplitude. For the tangent function, the amplitude is technically undefined because the function extends to infinity. However, the vertical stretch factor is |A|=1

3. Calculate the period using the formula P=π/|B|

P=π/3/5

P=(5*π)/3

4. Identify the phase shift. The phase shift is determined by the value of C in the horizontal shift component (x−C) Since there is no horizontal translation, the phase shift is 0

Final Answer

Amplitude: None (Stretch Factor: 1), Period: (5*π)/3*, Phase Shift: 0

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