Graph y=4cos(2(x-90))-2

Graph y=4cos(2(x-90))-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.
The absolute value is the distance between a number and zero. The distance between and is .
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:
Divide 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 each term.
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Simplify each term.
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Apply the distributive property.
Cancel the common factor of .
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Multiply by .
Subtract from .
Add and .
The exact value of is .
Multiply by .
Subtract from .
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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Simplify each term.
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Apply the distributive property.
Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Multiply by .
Subtract from .
Add and .
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 .
Subtract from .
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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Simplify each term.
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Apply the distributive property.
Cancel the common factor of .
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Multiply by .
Subtract from .
Add and .
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.
The exact value of is .
Multiply by .
Subtract from .
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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Simplify each term.
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Apply the distributive property.
Multiply by .
Subtract from .
Add and .
Subtract full rotations of until the angle is greater than or equal to and less than .
The exact value of is .
Multiply by .
Subtract from .
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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Simplify each term.
Tap for more steps...
Apply the distributive property.
Cancel the common factor of .
Tap for more steps...
Factor out of .
Cancel the common factor.
Rewrite the expression.
Multiply by .
Subtract from .
Add and .
Subtract full rotations of until the angle is greater than or equal to and less than .
The exact value of is .
Multiply by .
Subtract from .
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 six hundred nineteen million two hundred nineteen thousand six

Interesting facts

  • 1619219006 has 16 divisors, whose sum is 2476558800
  • The reverse of 1619219006 is 6009129161
  • Previous prime number is 1489

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 35
  • Digital Root 8

Name

Name one billion eight hundred fifty-seven million one hundred eighty-six thousand seven hundred seventy-one

Interesting facts

  • 1857186771 has 16 divisors, whose sum is 2499826848
  • The reverse of 1857186771 is 1776817581
  • Previous prime number is 941

Basic properties

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

Name

Name one billion three hundred ninety million five hundred ninety-two thousand eight hundred twenty-four

Interesting facts

  • 1390592824 has 64 divisors, whose sum is 4944531600
  • The reverse of 1390592824 is 4282950931
  • Previous prime number is 6493

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 43
  • Digital Root 7