# Graph 3sin(7x)

Graph 3sin(7x)
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.
The absolute value is the distance between a number and zero. The distance between and is .
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.
Multiply by .
The exact value of is .
Multiply by .
Find the point at .
Replace the variable with in the expression.
Simplify the result.
Cancel the common factor of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
The exact value of is .
Multiply by .
Find the point at .
Replace the variable with in the expression.
Simplify the result.
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
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.
Cancel the common factor of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
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.
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
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 eight hundred eighty-three million eight hundred thirty-eight thousand eight hundred sixty

### Interesting facts

• 883838860 has 32 divisors, whose sum is 2388757392
• The reverse of 883838860 is 068838388
• Previous prime number is 1021

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 52
• Digital Root 7

### Name

Name one billion thirteen million sixty-three thousand nine hundred seventy-five

### Interesting facts

• 1013063975 has 32 divisors, whose sum is 1623931200
• The reverse of 1013063975 is 5793603101
• Previous prime number is 5

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 35
• Digital Root 8

### Name

Name one billion five hundred thirty-three million six hundred ninety-three thousand five hundred eight

### Interesting facts

• 1533693508 has 16 divisors, whose sum is 3452413680
• The reverse of 1533693508 is 8053963351
• Previous prime number is 2179

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 43
• Digital Root 7