# Graph -3sin(3/2x)

Graph -3sin(3/2x)
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
Multiply the numerator by the reciprocal of the denominator.
Multiply .
Combine and .
Multiply by .
Combine and .
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:
Multiply 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.
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 .
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 .
Reduce the expression by cancelling the common factors.
Reduce the expression by cancelling the common factors.
Cancel the common factor.
Rewrite the expression.
Divide by .
The exact value of is .
Multiply by .
Find the point at .
Replace the variable with in the expression.
Simplify the result.
Combine and .
Multiply by .
Reduce the expression by cancelling the common factors.
Reduce the expression by cancelling the common factors.
Factor out of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Divide by .
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.
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.
Combine and .
Multiply by .
Reduce the expression by cancelling the common factors.
Reduce the expression by cancelling the common factors.
Factor out of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Divide by .
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 right)
Vertical Shift:
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### Name

Name two hundred seventy-six million one hundred thirteen thousand ninety-two

### Interesting facts

• 276113092 has 64 divisors, whose sum is 677160000
• The reverse of 276113092 is 290311672
• Previous prime number is 149

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 31
• Digital Root 4

### Name

Name four hundred ninety-one million four hundred forty-nine thousand two hundred eighty-one

### Interesting facts

• 491449281 has 32 divisors, whose sum is 686188800
• The reverse of 491449281 is 182944194
• Previous prime number is 109

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 9
• Sum of Digits 42
• Digital Root 6

### Name

Name one billion nine hundred seventy-four million three hundred twenty-one thousand one hundred fifty-eight

### Interesting facts

• 1974321158 has 8 divisors, whose sum is 2980345152
• The reverse of 1974321158 is 8511234791
• Previous prime number is 157

### Basic properties

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