Graph y=10cos(pix-pi/2)

Graph y=10cos(pix-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
Cancel the common factor of .
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Cancel the common factor.
Divide 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:
Cancel the common factor of .
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Cancel the common factor.
Phase Shift:
Rewrite the expression.
Phase Shift:
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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Combine and .
Combine the numerators over the common denominator.
Subtract from .
Divide 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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Multiply by .
To write as a fraction with a common denominator, multiply by .
Combine fractions.
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Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
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Move to the left of .
Subtract from .
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 each term.
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Combine and .
Move to the left of .
Simplify terms.
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Combine the numerators over the common denominator.
Subtract from .
Cancel the common factor of .
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Cancel the common factor.
Divide by .
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 .
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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Move to the left of .
To write as a fraction with a common denominator, multiply by .
Combine fractions.
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Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
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Multiply by .
Subtract from .
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.
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 each term.
Tap for more steps...
Combine and .
Move to the left of .
Simplify terms.
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Combine the numerators over the common denominator.
Subtract from .
Cancel the common factor of and .
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Factor out of .
Cancel the common factors.
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Divide by .
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 twenty-eight million nine hundred forty-four thousand seven hundred fifty-four

Interesting facts

  • 1028944754 has 16 divisors, whose sum is 1640121048
  • The reverse of 1028944754 is 4574498201
  • Previous prime number is 277

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 44
  • Digital Root 8

Name

Name seven hundred thirty-nine million one hundred thirty-five thousand thirty-two

Interesting facts

  • 739135032 has 128 divisors, whose sum is 3427466400
  • The reverse of 739135032 is 230531937
  • Previous prime number is 89

Basic properties

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

Name

Name one billion one hundred fifteen million three hundred forty-three thousand nine hundred twenty-eight

Interesting facts

  • 1115343928 has 32 divisors, whose sum is 3962406600
  • The reverse of 1115343928 is 8293435111
  • Previous prime number is 19

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 37
  • Digital Root 1