Graph y=cos(5x)

Graph y=cos(5x)
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 .
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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Multiply by .
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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Cancel the common factor of .
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Factor out of .
Cancel the common factor.
Rewrite the expression.
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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Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
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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Cancel the common factor of .
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Factor out of .
Cancel the common factor.
Rewrite the expression.
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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Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
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 two hundred forty-five million two hundred seventy-five thousand eight hundred ninety-nine

Interesting facts

  • 1245275899 has 8 divisors, whose sum is 1446503648
  • The reverse of 1245275899 is 9985725421
  • Previous prime number is 61

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 52
  • Digital Root 7

Name

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

Interesting facts

  • 1436282126 has 4 divisors, whose sum is 2154423192
  • The reverse of 1436282126 is 6212826341
  • Previous prime number is 2

Basic properties

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

Name

Name four hundred eight million seven hundred fifty-seven thousand six hundred four

Interesting facts

  • 408757604 has 16 divisors, whose sum is 925796736
  • The reverse of 408757604 is 406757804
  • Previous prime number is 151

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 41
  • Digital Root 5