Graph y=cos(1/6x)

Graph y=cos(1/6x)
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.
is approximately which is positive so remove the absolute value
Multiply the numerator by the reciprocal of the denominator.
Multiply 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:
Multiply the numerator by the reciprocal of the denominator.
Phase Shift:
Multiply 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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Divide 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 and .
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Factor out of .
Cancel the common factors.
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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.
Divide by .
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 and .
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Factor out of .
Cancel the common factors.
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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 and .
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Factor out of .
Cancel the common factors.
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Divide by .
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 eight hundred ninety-eight million nine hundred eleven thousand three hundred forty-four

Interesting facts

  • 898911344 has 32 divisors, whose sum is 4550738760
  • The reverse of 898911344 is 443119898
  • Previous prime number is 2

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 47
  • Digital Root 2

Name

Name one billion seven hundred fifty-five million six hundred thirty-nine thousand one hundred thirty-six

Interesting facts

  • 1755639136 has 64 divisors, whose sum is 13331884932
  • The reverse of 1755639136 is 6319365571
  • Previous prime number is 2

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 46
  • Digital Root 1

Name

Name three hundred seven million three hundred seventy-one thousand four hundred forty-eight

Interesting facts

  • 307371448 has 64 divisors, whose sum is 1117421568
  • The reverse of 307371448 is 844173703
  • Previous prime number is 31

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 37
  • Digital Root 1