# Graph g(x)=4sin(pix)-3

Graph g(x)=4sin(pix)-3
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:
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.
Find the point at .
Replace the variable with in the expression.
Simplify the result.
Simplify each term.
Multiply by .
The exact value of is .
Multiply by .
Subtract from .
Find the point at .
Replace the variable with in the expression.
Simplify the result.
Simplify each term.
Combine and .
The exact value of is .
Multiply by .
Subtract from .
Find the point at .
Replace the variable with in the expression.
Simplify the result.
Simplify each term.
Multiply by .
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.
The exact value of is .
Multiply by .
Subtract from .
Find the point at .
Replace the variable with in the expression.
Simplify the result.
Simplify each term.
Combine and .
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 .
Subtract from .
Find the point at .
Replace the variable with in the expression.
Simplify the result.
Simplify each term.
Move to the left of .
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 .
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 fifty-eight million two hundred twenty-nine thousand seven hundred fifty-three

### Interesting facts

• 58229753 has 4 divisors, whose sum is 58332660
• The reverse of 58229753 is 35792285
• Previous prime number is 569

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 8
• Sum of Digits 41
• Digital Root 5

### Name

Name one billion six hundred eighty-one million seven hundred forty-six thousand four hundred forty-seven

### Interesting facts

• 1681746447 has 8 divisors, whose sum is 2246062000
• The reverse of 1681746447 is 7446471861
• Previous prime number is 601

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 48
• Digital Root 3

### Name

Name seven hundred thirty-nine million six hundred eighty-seven thousand three hundred eighty-two

### Interesting facts

• 739687382 has 16 divisors, whose sum is 1268468640
• The reverse of 739687382 is 283786937
• Previous prime number is 3677

### Basic properties

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