# 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 nine hundred seventy-four million eight hundred thirty-five thousand seven hundred thirty-two

### Interesting facts

• 1974835732 has 8 divisors, whose sum is 4443380406
• The reverse of 1974835732 is 2375384791
• Previous prime number is 2

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 49
• Digital Root 4

### Name

Name seven hundred fifty-five million four hundred thirty-two thousand four hundred forty-three

### Interesting facts

• 755432443 has 4 divisors, whose sum is 756575968
• The reverse of 755432443 is 344234557
• Previous prime number is 661

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 9
• Sum of Digits 37
• Digital Root 1

### Name

Name one billion seven hundred thirty-one million one hundred fifty-three thousand nine hundred forty-four

### Interesting facts

• 1731153944 has 32 divisors, whose sum is 6292079136
• The reverse of 1731153944 is 4493511371
• Previous prime number is 13

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 38
• Digital Root 2