# 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 .
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 .
Cancel the common factor.
Divide by .
Find the phase shift using the formula .
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 .
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.
Find the point at .
Replace the variable with in the expression.
Simplify the result.
Combine and .
Combine the numerators over the common denominator.
Divide by .
The exact value of is .
Multiply by .
Find the point at .
Replace the variable with in the expression.
Simplify the result.
Multiply by .
The exact value of is .
Multiply by .
Find the point at .
Replace the variable with in the expression.
Simplify the result.
Combine and .
Combine the numerators over the common denominator.
Cancel the common factor of .
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 .
Find the point at .
Replace the variable with in the expression.
Simplify the result.
Multiply by .
To write as a fraction with a common denominator, multiply by .
Combine fractions.
Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
Move to the left of .
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 .
Find the point at .
Replace the variable with in the expression.
Simplify the result.
Simplify each term.
Combine and .
Move to the left of .
Simplify terms.
Combine the numerators over the common denominator.
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
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 .
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 ninety-four million three hundred sixty thousand two hundred nineteen

### Interesting facts

• 94360219 has 4 divisors, whose sum is 94381144
• The reverse of 94360219 is 91206349
• Previous prime number is 6577

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 8
• Sum of Digits 34
• Digital Root 7

### Name

Name one billion seven hundred ninety-four million two hundred eleven thousand nine hundred seventy-nine

### Interesting facts

• 1794211979 has 16 divisors, whose sum is 2346451968
• The reverse of 1794211979 is 9791124971
• Previous prime number is 797

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 50
• Digital Root 5

### Name

Name two hundred ninety-three million three hundred fifty-eight thousand one hundred sixty-eight

### Interesting facts

• 293358168 has 32 divisors, whose sum is 1100093400
• The reverse of 293358168 is 861853392
• Previous prime number is 9

### Basic properties

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