Graph f(x)=-3sin(2x-pi)

Graph f(x)=-3sin(2x-pi)
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 .
Cancel the common factor of .
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Cancel the common factor.
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:
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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Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Subtract from .
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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Factor out of .
Cancel the common factor.
Rewrite the expression.
To write as a fraction with a common denominator, multiply by .
Combine fractions.
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Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
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Multiply by .
Subtract from .
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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Subtract from .
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 .
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Factor out of .
Cancel the common factor.
Rewrite the expression.
To write as a fraction with a common denominator, multiply by .
Combine fractions.
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Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
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Multiply by .
Subtract from .
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 .
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.
Rewrite the expression.
Subtract from .
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 one billion two hundred fifteen million seven hundred ninety-three thousand eight hundred fifty

Interesting facts

  • 1215793850 has 128 divisors, whose sum is 2933280000
  • The reverse of 1215793850 is 0583975121
  • Previous prime number is 193

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 41
  • Digital Root 5

Name

Name one billion six hundred eighty-one million five hundred fifty-three thousand three hundred seventy-one

Interesting facts

  • 1681553371 has 8 divisors, whose sum is 1831093200
  • The reverse of 1681553371 is 1733551861
  • Previous prime number is 29

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 40
  • Digital Root 4

Name

Name three hundred seven million three hundred eighty-three thousand two hundred one

Interesting facts

  • 307383201 has 32 divisors, whose sum is 558579840
  • The reverse of 307383201 is 102383703
  • Previous prime number is 137

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 9
  • Sum of Digits 27
  • Digital Root 9