Find Amplitude, Period, and Phase Shift y=sin((8pix)/3+pi/2)

Find Amplitude, Period, and Phase Shift y=sin((8pix)/3+pi/2)
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 of .
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The period of the function can be calculated using .
Replace with in the formula for period.
is approximately which is positive so remove the absolute value
Multiply the numerator by the reciprocal of the denominator.
Cancel the common factor of .
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Find the phase shift using the formula .
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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:
Cancel the common factor of .
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Move the leading negative in into the numerator.
Phase Shift:
Factor out of .
Phase Shift:
Factor out of .
Phase Shift:
Cancel the common factor.
Phase Shift:
Rewrite the expression.
Phase Shift:
Phase Shift:
Multiply and .
Phase Shift:
Simplify the expression.
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Multiply by .
Phase Shift:
Multiply by .
Phase Shift:
Move the negative in front of the fraction.
Phase Shift:
Phase Shift:
Phase Shift:
List the properties of the trigonometric function.
Amplitude:
Period:
Phase Shift: ( to the left)
Vertical Shift: None
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Name

Name one billion eight hundred twenty-nine million nine hundred twelve thousand four hundred nine

Interesting facts

  • 1829912409 has 8 divisors, whose sum is 2189638920
  • The reverse of 1829912409 is 9042199281
  • Previous prime number is 13

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 45
  • Digital Root 9

Name

Name nine hundred fourteen million two hundred sixty thousand five hundred twenty-four

Interesting facts

  • 914260524 has 32 divisors, whose sum is 2747234880
  • The reverse of 914260524 is 425062419
  • Previous prime number is 619

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 33
  • Digital Root 6

Name

Name one billion six hundred thirty million one hundred eight thousand one hundred twenty

Interesting facts

  • 1630108120 has 64 divisors, whose sum is 6685519680
  • The reverse of 1630108120 is 0218010361
  • Previous prime number is 79

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 22
  • Digital Root 4