# 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 six hundred twelve million eight hundred eight thousand seven hundred two

### Interesting facts

• 612808702 has 8 divisors, whose sum is 1002777912
• The reverse of 612808702 is 207808216
• Previous prime number is 11

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 34
• Digital Root 7

### Name

Name one billion four hundred sixty-four million eight hundred seventy-seven thousand nine hundred seventy

### Interesting facts

• 1464877970 has 16 divisors, whose sum is 2642877720
• The reverse of 1464877970 is 0797784641
• Previous prime number is 433

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 53
• Digital Root 8

### Name

Name six hundred eighty-seven million eighty-six thousand two hundred seventy

### Interesting facts

• 687086270 has 64 divisors, whose sum is 1401624000
• The reverse of 687086270 is 072680786
• Previous prime number is 59

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 44
• Digital Root 8