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 four hundred eighty-six million seven hundred thirty-six thousand three hundred forty-six

Interesting facts

  • 486736346 has 4 divisors, whose sum is 730104522
  • The reverse of 486736346 is 643637684
  • Previous prime number is 2

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 47
  • Digital Root 2

Name

Name one billion three hundred thirty-six million nine hundred sixty-eight thousand four hundred eighty-nine

Interesting facts

  • 1336968489 has 8 divisors, whose sum is 1785759840
  • The reverse of 1336968489 is 9848696331
  • Previous prime number is 569

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 57
  • Digital Root 3

Name

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

Interesting facts

  • 221350783 has 4 divisors, whose sum is 222058288
  • The reverse of 221350783 is 387053122
  • Previous prime number is 313

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 9
  • Sum of Digits 31
  • Digital Root 4