Find Amplitude, Period, and Phase Shift y=cos((6pix)/7+pi/2)

Find Amplitude, Period, and Phase Shift y=cos((6pix)/7+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 three hundred eighty-five million five hundred seventeen thousand eight hundred twenty-seven

Interesting facts

  • 1385517827 has 8 divisors, whose sum is 1432103280
  • The reverse of 1385517827 is 7287155831
  • Previous prime number is 61

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 47
  • Digital Root 2

Name

Name one billion six hundred ninety-five million fifty-four thousand eight hundred seventy-six

Interesting facts

  • 1695054876 has 16 divisors, whose sum is 5085164664
  • The reverse of 1695054876 is 6784505961
  • Previous prime number is 3

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 51
  • Digital Root 6

Name

Name seven hundred sixteen million two hundred fifty-three thousand one hundred twenty-three

Interesting facts

  • 716253123 has 8 divisors, whose sum is 956920000
  • The reverse of 716253123 is 321352617
  • Previous prime number is 499

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 9
  • Sum of Digits 30
  • Digital Root 3