Graph y=2cos(x/4)

Graph y=2cos(x/4)
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 .
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.
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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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 .
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 .
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.
Divide by .
Subtract full rotations of until the angle is greater than or equal to and less than .
The exact value of is .
Multiply by .
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 nine hundred sixty-three million two hundred fifty-two thousand three hundred sixty-three

Interesting facts

  • 963252363 has 8 divisors, whose sum is 1286150800
  • The reverse of 963252363 is 363252369
  • Previous prime number is 709

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 9
  • Sum of Digits 39
  • Digital Root 3

Name

Name one billion two hundred eighty-nine million twenty-three thousand one hundred ninety-four

Interesting facts

  • 1289023194 has 16 divisors, whose sum is 2713733280
  • The reverse of 1289023194 is 4913209821
  • Previous prime number is 19

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 39
  • Digital Root 3

Name

Name three hundred twenty-seven million two hundred thirteen thousand four hundred thirty-six

Interesting facts

  • 327213436 has 32 divisors, whose sum is 820253952
  • The reverse of 327213436 is 634312723
  • Previous prime number is 11

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 31
  • Digital Root 4