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 six hundred eighty-six million nine hundred forty-three thousand eight hundred thirty

Interesting facts

  • 1686943830 has 64 divisors, whose sum is 3637460736
  • The reverse of 1686943830 is 0383496861
  • Previous prime number is 11

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 48
  • Digital Root 3

Name

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

Interesting facts

  • 1446236684 has 8 divisors, whose sum is 3254032548
  • The reverse of 1446236684 is 4866326441
  • Previous prime number is 2

Basic properties

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

Name

Name one billion seven hundred sixteen million five hundred seventy-eight thousand thirty-six

Interesting facts

  • 1716578036 has 16 divisors, whose sum is 3862748736
  • The reverse of 1716578036 is 6308756171
  • Previous prime number is 11087

Basic properties

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