Graph sin(2x)-sin(5x)

Graph sin(2x)-sin(5x)
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:
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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Simplify each term.
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Multiply by .
The exact value of is .
Multiply 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.
The exact value of is .
Combine and .
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 third quadrant.
The exact value of is .
Multiply .
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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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Simplify each term.
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Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.
The exact value of is .
Combine and .
Subtract full rotations of until the angle is greater than or equal to and less than .
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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Cancel the common factor of .
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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 .
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Combine and .
Multiply by .
Subtract full rotations of until the angle is greater than or equal to and less than .
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 .
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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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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 .
Subtract full rotations of until the angle is greater than or equal to and less than .
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 .
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 nine hundred forty-three million nine hundred nine thousand seventy-three

Interesting facts

  • 1943909073 has 4 divisors, whose sum is 2159898980
  • The reverse of 1943909073 is 3709093491
  • Previous prime number is 9

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 45
  • Digital Root 9

Name

Name three hundred ninety-eight million one hundred seventy-seven thousand six hundred ninety-three

Interesting facts

  • 398177693 has 4 divisors, whose sum is 398516028
  • The reverse of 398177693 is 396771893
  • Previous prime number is 1181

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 9
  • Sum of Digits 53
  • Digital Root 8

Name

Name one billion one hundred forty-three million nine hundred sixty-one thousand two hundred sixty-five

Interesting facts

  • 1143961265 has 8 divisors, whose sum is 1378646568
  • The reverse of 1143961265 is 5621693411
  • Previous prime number is 233

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 38
  • Digital Root 2