Find Amplitude, Period, and Phase Shift f(t)=25sin(160pit)+115

Find Amplitude, Period, and Phase Shift f(t)=25sin(160pit)+115
Use the form to find the variables used to find the amplitude, period, phase shift, and vertical shift.
Find the amplitude .
Amplitude:
Find the period using the formula .
The period of the function can be calculated using .
Period:
Replace with in the formula for period.
Period:
Solve the equation.
is approximately which is positive so remove the absolute value
Period:
Cancel the common factor of and .
Factor out of .
Period:
Cancel the common factors.
Factor out of .
Period:
Cancel the common factor.
Period:
Rewrite the expression.
Period:
Period:
Period:
Cancel the common factor of .
Cancel the common factor.
Period:
Rewrite the expression.
Period:
Period:
Period:
Period:
Find the phase shift using the formula .
The phase shift of the function can be calculated from .
Phase Shift:
Replace the values of and in the equation for phase shift.
Phase Shift:
Cancel the common factor of and .
Factor out of .
Phase Shift:
Cancel the common factors.
Factor out of .
Phase Shift:
Cancel the common factor.
Phase Shift:
Rewrite the expression.
Phase Shift:
Phase Shift:
Phase Shift:
Divide by .
Phase Shift:
Phase Shift:
Find the vertical shift .
Vertical Shift:
List the properties of the trigonometric function.
Amplitude:
Period:
Phase Shift: ( to the right)
Vertical Shift:
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Name

Name eight hundred eighty-six million seven hundred twenty-nine thousand nine hundred forty-one

Interesting facts

• 886729941 has 4 divisors, whose sum is 985255500
• The reverse of 886729941 is 149927688
• Previous prime number is 9

Basic properties

• Is Prime? no
• Number parity odd
• Number length 9
• Sum of Digits 54
• Digital Root 9

Name

Name six hundred sixty-eight million two hundred seventeen thousand two hundred fifty-three

Interesting facts

• 668217253 has 8 divisors, whose sum is 738950976
• The reverse of 668217253 is 352712866
• Previous prime number is 73

Basic properties

• Is Prime? no
• Number parity odd
• Number length 9
• Sum of Digits 40
• Digital Root 4

Name

Name one hundred thirty-five million seven hundred forty-seven thousand seven hundred fifty-nine

Interesting facts

• 135747759 has 8 divisors, whose sum is 206853760
• The reverse of 135747759 is 957747531
• Previous prime number is 7

Basic properties

• Is Prime? no
• Number parity odd
• Number length 9
• Sum of Digits 48
• Digital Root 3