Graph y=2sin(3(x+pi/12))+4

Graph y=2sin(3(x+pi/12))+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.
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:
Multiply the numerator by the reciprocal of the denominator.
Phase Shift:
Multiply .
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Multiply and .
Phase Shift:
Multiply by .
Phase Shift:
Phase Shift:
Phase Shift:
Find the vertical shift .
Vertical Shift:
List the properties of the trigonometric function.
Amplitude:
Period:
Phase Shift: ( to the left)
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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Simplify each term.
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Simplify each term.
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Cancel the common factor of .
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Move the leading negative in into the numerator.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Move the negative in front of the fraction.
Combine the numerators over the common denominator.
Add and .
Divide by .
The exact value of is .
Multiply by .
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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Cancel the common factor of .
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Combine the numerators over the common denominator.
Add and .
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 .
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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Combine and .
Combine the numerators over the common denominator.
Add and .
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.
The exact value of is .
Multiply by .
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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Cancel the common factor of .
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Combine the numerators over the common denominator.
Add and .
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. Make the expression negative because sine is negative in the fourth quadrant.
The exact value of is .
Multiply by .
Multiply by .
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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Cancel the common factor of .
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Combine the numerators over the common denominator.
Add and .
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 .
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 left)
Vertical Shift:
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Name

Name four hundred twenty million five hundred ninety-five thousand one hundred sixty-five

Interesting facts

  • 420595165 has 4 divisors, whose sum is 504714204
  • The reverse of 420595165 is 561595024
  • Previous prime number is 5

Basic properties

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

Name

Name two billion thirty-six million two hundred twenty-two thousand four hundred eighty-two

Interesting facts

  • 2036222482 has 8 divisors, whose sum is 3490667136
  • The reverse of 2036222482 is 2842226302
  • Previous prime number is 7

Basic properties

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

Name

Name nine hundred thirty-one million six hundred ninety-six thousand nine hundred ninety-five

Interesting facts

  • 931696995 has 32 divisors, whose sum is 1574318592
  • The reverse of 931696995 is 599696139
  • Previous prime number is 83

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 9
  • Sum of Digits 57
  • Digital Root 3