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 seventy-three million seven thousand five hundred sixty-five

Interesting facts

  • 73007565 has 8 divisors, whose sum is 116812128
  • The reverse of 73007565 is 56570037
  • Previous prime number is 5

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 8
  • Sum of Digits 33
  • Digital Root 6

Name

Name eight hundred seven million nine hundred ninety-three thousand six hundred nine

Interesting facts

  • 807993609 has 8 divisors, whose sum is 1077543360
  • The reverse of 807993609 is 906399708
  • Previous prime number is 5479

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 9
  • Sum of Digits 51
  • Digital Root 6

Name

Name one billion seven hundred thirty million sixty-two thousand one hundred thirty-eight

Interesting facts

  • 1730062138 has 16 divisors, whose sum is 2616846336
  • The reverse of 1730062138 is 8312600371
  • Previous prime number is 3911

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 31
  • Digital Root 4