Graph r=2+cos(x)

Graph r=2+cos(x)
Rewrite the expression as .
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 .
Add and .
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 .
Add and .
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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Simplify each term.
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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 .
Subtract from .
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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Simplify each term.
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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 .
Add and .
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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Simplify each term.
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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 .
Add and .
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 four hundred sixty-two million three hundred seven thousand one hundred forty-three

Interesting facts

  • 1462307143 has 16 divisors, whose sum is 1628904960
  • The reverse of 1462307143 is 3417032641
  • Previous prime number is 79

Basic properties

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

Name

Name ninety-six million four hundred thirty-four thousand nine hundred nineteen

Interesting facts

  • 96434919 has 8 divisors, whose sum is 122457120
  • The reverse of 96434919 is 91943469
  • Previous prime number is 7

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 8
  • Sum of Digits 45
  • Digital Root 9

Name

Name nine hundred thirty-six million four hundred ninety-one thousand seven hundred eighty-nine

Interesting facts

  • 936491789 has 4 divisors, whose sum is 943229280
  • The reverse of 936491789 is 987194639
  • Previous prime number is 139

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 9
  • Sum of Digits 56
  • Digital Root 2