# Graph f(x)=-sin(2x)

Graph f(x)=-sin(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.
The absolute value is the distance between a number and zero. The distance between and is .
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.
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 .
Find the point at .
Replace the variable with in the expression.
Simplify the result.
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 one billion two hundred twenty-one million eight hundred sixteen thousand forty

### Interesting facts

• 1221816040 has 128 divisors, whose sum is 5006935296
• The reverse of 1221816040 is 0406181221
• Previous prime number is 541

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 25
• Digital Root 7

### Name

Name two billion ninety-three million four hundred forty-five thousand five hundred forty-four

### Interesting facts

• 2093445544 has 32 divisors, whose sum is 7074806976
• The reverse of 2093445544 is 4455443902
• Previous prime number is 751

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 40
• Digital Root 4

### Name

Name one billion five hundred twenty-seven million eight hundred twenty thousand five hundred sixty-eight

### Interesting facts

• 1527820568 has 32 divisors, whose sum is 5202029304
• The reverse of 1527820568 is 8650287251
• Previous prime number is 113

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 44
• Digital Root 8