Graph y=9/5*cos(-(3pi)/2x)

Graph y=9/5*cos(-(3pi)/2x)
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 .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Combine and .
Multiply by .
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:
Multiply 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:
Select a few points to graph.
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Find the point at .
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Replace the variable with in the expression.
Simplify the result.
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Simplify the numerator.
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Multiply by .
Multiply by .
The exact value of is .
Multiply by .
The final answer is .
Find the point at .
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Replace the variable with in the expression.
Simplify the result.
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Simplify the numerator.
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Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Multiply by .
The exact value of is .
Simplify the expression.
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Multiply by .
Divide by .
The final answer is .
Find the point at .
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Replace the variable with in the expression.
Simplify the result.
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Simplify the numerator.
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Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the second quadrant.
The exact value of is .
Multiply by .
Simplify the expression.
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Multiply by .
Move the negative in front of the fraction.
The final answer is .
Find the point at .
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Replace the variable with in the expression.
Simplify the result.
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Simplify the numerator.
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Multiply by .
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.
The exact value of is .
Simplify the expression.
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Multiply by .
Divide by .
The final answer is .
Find the point at .
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Replace the variable with in the expression.
Simplify the result.
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Simplify the numerator.
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Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Subtract full rotations of until the angle is greater than or equal to and less than .
The exact value of is .
Multiply by .
The final answer is .
List the points in a table.
The trig function can be graphed using the amplitude, period, phase shift, vertical shift, and the points.
Amplitude:
Period:
Phase Shift: ( to the right)
Vertical Shift:
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Name

Name one billion four hundred thirty-six million two hundred forty-two thousand six hundred

Interesting facts

  • 1436242600 has 128 divisors, whose sum is 7517086416
  • The reverse of 1436242600 is 0062426341
  • Previous prime number is 5

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 28
  • Digital Root 1

Name

Name two hundred eighty-six million eleven thousand six hundred fifty-one

Interesting facts

  • 286011651 has 8 divisors, whose sum is 381664080
  • The reverse of 286011651 is 156110682
  • Previous prime number is 1229

Basic properties

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

Name

Name one hundred fifty-one million four hundred nineteen thousand three hundred thirty-two

Interesting facts

  • 151419332 has 16 divisors, whose sum is 340828992
  • The reverse of 151419332 is 233914151
  • Previous prime number is 3191

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 29
  • Digital Root 2