Find Amplitude, Period, and Phase Shift y=5sin((2x)/3-pi)

Find Amplitude, Period, and Phase Shift y=5sin((2x)/3-pi)
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:
Multiply the numerator by the reciprocal of the denominator.
Period:
Cancel the common factor of .
Factor out of .
Period:
Cancel the common factor.
Period:
Rewrite the expression.
Period:
Period:
Move to the left of .
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:
Multiply the numerator by the reciprocal of the denominator.
Phase Shift:
Combine and .
Phase Shift:
Move to the left of .
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 one hundred eighty-two million one hundred forty-seven thousand eight hundred thirty-four

Interesting facts

• 182147834 has 32 divisors, whose sum is 326140992
• The reverse of 182147834 is 438741281
• Previous prime number is 401

Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 38
• Digital Root 2

Name

Name one billion six hundred fifty-five million twenty-two thousand two hundred eight

Interesting facts

• 1655022208 has 2048 divisors, whose sum is 34549701120
• The reverse of 1655022208 is 8022205561
• Previous prime number is 67

Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 31
• Digital Root 4

Name

Name one billion eight hundred twenty-two million four hundred sixteen thousand seven hundred five

Interesting facts

• 1822416705 has 16 divisors, whose sum is 2167578880
• The reverse of 1822416705 is 5076142281
• Previous prime number is 283

Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 36
• Digital Root 9