Trigonometry Examples

Find Amplitude, Period, and Phase Shift 5tan(1/3x+pi/2)
Step 1
Use the form to find the variables used to find the amplitude, period, phase shift, and vertical shift.
Step 2
Since the graph of the function does not have a maximum or minimum value, there can be no value for the amplitude.
Amplitude: None
Step 3
Find the period of .
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Step 3.1
The period of the function can be calculated using .
Step 3.2
Replace with in the formula for period.
Step 3.3
is approximately which is positive so remove the absolute value
Step 3.4
Multiply the numerator by the reciprocal of the denominator.
Step 3.5
Move to the left of .
Step 4
Find the phase shift using the formula .
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Step 4.1
The phase shift of the function can be calculated from .
Phase Shift:
Step 4.2
Replace the values of and in the equation for phase shift.
Phase Shift:
Step 4.3
Multiply the numerator by the reciprocal of the denominator.
Phase Shift:
Step 4.4
Multiply .
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Step 4.4.1
Multiply by .
Phase Shift:
Step 4.4.2
Combine and .
Phase Shift:
Phase Shift:
Step 4.5
Move the negative in front of the fraction.
Phase Shift:
Phase Shift:
Step 5
List the properties of the trigonometric function.
Amplitude: None
Period:
Phase Shift: ( to the left)
Vertical Shift: None
Step 6