Graph y=3sin(pix+pi/2)

Graph y=3sin(pix+pi/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
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:
Multiply the numerator by the reciprocal of the denominator.
Phase Shift:
Cancel the common factor of .
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Move the leading negative in into the numerator.
Phase Shift:
Factor out of .
Phase Shift:
Cancel the common factor.
Phase Shift:
Rewrite the expression.
Phase Shift:
Phase Shift:
Move the negative in front of the fraction.
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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Combine and .
Combine the numerators over the common denominator.
Add and .
Divide by .
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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Multiply by .
Add and .
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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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 .
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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Multiply by .
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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Move to the left of .
Add 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 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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Simplify each term.
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Combine and .
Move to the left of .
Simplify terms.
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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 .
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 two billion twenty-one million one hundred forty-nine thousand five hundred thirteen

Interesting facts

  • 2021149513 has 4 divisors, whose sum is 2022876688
  • The reverse of 2021149513 is 3159411202
  • Previous prime number is 1171

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 28
  • Digital Root 1

Name

Name one billion six hundred fifteen million five hundred forty-seven thousand four hundred

Interesting facts

  • 1615547400 has 256 divisors, whose sum is 8066822400
  • The reverse of 1615547400 is 0047455161
  • Previous prime number is 149

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 33
  • Digital Root 6

Name

Name six hundred twenty-eight million five hundred eighty-five thousand six hundred twenty-eight

Interesting facts

  • 628585628 has 32 divisors, whose sum is 1543916160
  • The reverse of 628585628 is 826585826
  • Previous prime number is 1879

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 50
  • Digital Root 5