Graph cos(0-a)

Graph cos(0-a)
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 .
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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The exact value of is .
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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The exact value of is .
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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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 .
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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Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.
The exact value of is .
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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Subtract full rotations of until the angle is greater than or equal to and less than .
The exact value of is .
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 eight hundred seventeen million eight hundred seventy-four thousand one hundred ninety-four

Interesting facts

  • 1817874194 has 4 divisors, whose sum is 2726811294
  • The reverse of 1817874194 is 4914787181
  • Previous prime number is 2

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 50
  • Digital Root 5

Name

Name two billion ninety-eight million eight hundred thirty-nine thousand nine hundred twenty-one

Interesting facts

  • 2098839921 has 16 divisors, whose sum is 3100780800
  • The reverse of 2098839921 is 1299388902
  • Previous prime number is 19

Basic properties

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

Name

Name one billion two hundred twenty-four million sixty-one thousand eight hundred twenty-seven

Interesting facts

  • 1224061827 has 4 divisors, whose sum is 1632082440
  • The reverse of 1224061827 is 7281604221
  • Previous prime number is 3

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 33
  • Digital Root 6