Trigonometry Examples

Find Amplitude, Period, and Phase Shift y=3sin(2pix+4)
Step 1
Use the form to find the variables used to find the amplitude, period, phase shift, and vertical shift.
Step 2
Find the amplitude .
Amplitude:
Step 3
Find the period of .
Tap for more steps...
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
Cancel the common factor of .
Tap for more steps...
Step 3.4.1
Cancel the common factor.
Step 3.4.2
Rewrite the expression.
Step 3.5
Cancel the common factor of .
Tap for more steps...
Step 3.5.1
Cancel the common factor.
Step 3.5.2
Rewrite the expression.
Step 4
Find the phase shift using the formula .
Tap for more steps...
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
Cancel the common factor of and .
Tap for more steps...
Step 4.3.1
Factor out of .
Phase Shift:
Step 4.3.2
Cancel the common factors.
Tap for more steps...
Step 4.3.2.1
Factor out of .
Phase Shift:
Step 4.3.2.2
Cancel the common factor.
Phase Shift:
Step 4.3.2.3
Rewrite the expression.
Phase Shift:
Phase Shift:
Phase Shift:
Step 4.4
Move the negative in front of the fraction.
Phase Shift:
Phase Shift:
Step 5
List the properties of the trigonometric function.
Amplitude:
Period:
Phase Shift: ( to the left)
Vertical Shift: None
Step 6