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 two billion five million six hundred twenty-seven thousand sixty-two

Interesting facts

  • 2005627062 has 8 divisors, whose sum is 4011254136
  • The reverse of 2005627062 is 2607265002
  • Previous prime number is 3

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 30
  • Digital Root 3

Name

Name one billion five hundred seventeen million seven hundred thirty thousand seven hundred sixty-five

Interesting facts

  • 1517730765 has 8 divisors, whose sum is 2428369248
  • The reverse of 1517730765 is 5670377151
  • Previous prime number is 5

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 42
  • Digital Root 6

Name

Name two hundred seventy million six hundred twenty-three thousand nine hundred fifty-three

Interesting facts

  • 270623953 has 4 divisors, whose sum is 271630260
  • The reverse of 270623953 is 359326072
  • Previous prime number is 269

Basic properties

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