Trigonometry Examples

Find Amplitude, Period, and Phase Shift y=1+3sin(2(x+pi/2))
Step 1
Rewrite the expression as .
Step 2
Use the form to find the variables used to find the amplitude, period, phase shift, and vertical shift.
Step 3
Find the amplitude .
Amplitude:
Step 4
Find the period using the formula .
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Step 4.1
Find the period of .
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Step 4.1.1
The period of the function can be calculated using .
Step 4.1.2
Replace with in the formula for period.
Step 4.1.3
The absolute value is the distance between a number and zero. The distance between and is .
Step 4.1.4
Cancel the common factor of .
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Step 4.1.4.1
Cancel the common factor.
Step 4.1.4.2
Divide by .
Step 4.2
Find the period of .
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Step 4.2.1
The period of the function can be calculated using .
Step 4.2.2
Replace with in the formula for period.
Step 4.2.3
The absolute value is the distance between a number and zero. The distance between and is .
Step 4.2.4
Cancel the common factor of .
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Step 4.2.4.1
Cancel the common factor.
Step 4.2.4.2
Divide by .
Step 4.3
The period of addition/subtraction of trig functions is the maximum of the individual periods.
Step 5
Find the phase shift using the formula .
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Step 5.1
The phase shift of the function can be calculated from .
Phase Shift:
Step 5.2
Replace the values of and in the equation for phase shift.
Phase Shift:
Step 5.3
Move the negative in front of the fraction.
Phase Shift:
Phase Shift:
Step 6
List the properties of the trigonometric function.
Amplitude:
Period:
Phase Shift: ( to the left)
Vertical Shift:
Step 7