Graph y=4sin(x)

Graph y=4sin(x)
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 .
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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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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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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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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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 one hundred twenty-four million seven hundred fifty-nine thousand three hundred sixty-three

Interesting facts

  • 1124759363 has 32 divisors, whose sum is 1450939392
  • The reverse of 1124759363 is 3639574211
  • Previous prime number is 251

Basic properties

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

Name

Name eight hundred twenty-four million nine hundred twenty-six thousand eighty-seven

Interesting facts

  • 824926087 has 4 divisors, whose sum is 831421696
  • The reverse of 824926087 is 780629428
  • Previous prime number is 127

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 9
  • Sum of Digits 46
  • Digital Root 1

Name

Name two billion one hundred thirty-nine million one hundred fourteen thousand forty-two

Interesting facts

  • 2139114042 has 32 divisors, whose sum is 3661200000
  • The reverse of 2139114042 is 2404119312
  • Previous prime number is 2699

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 27
  • Digital Root 9