Graph y=3sin(1/2x)+2

Graph y=3sin(1/2x)+2
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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Simplify each term.
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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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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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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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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 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 right)
Vertical Shift:
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Name

Name five hundred fifty-eight million four hundred eighty-two thousand seven hundred twenty

Interesting facts

  • 558482720 has 128 divisors, whose sum is 5089175244
  • The reverse of 558482720 is 027284855
  • Previous prime number is 5

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 41
  • Digital Root 5

Name

Name one billion eight hundred eighty-six million two hundred fifty-four thousand one hundred eighty-six

Interesting facts

  • 1886254186 has 16 divisors, whose sum is 2859030720
  • The reverse of 1886254186 is 6814526881
  • Previous prime number is 311

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 49
  • Digital Root 4

Name

Name five hundred sixty-five million three hundred fourteen thousand seven hundred forty-nine

Interesting facts

  • 565314749 has 8 divisors, whose sum is 581555040
  • The reverse of 565314749 is 947413565
  • Previous prime number is 619

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 9
  • Sum of Digits 44
  • Digital Root 8