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

Graph f(x)=sin(2x-pi)
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:
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 .
Cancel the common factor.
Rewrite the expression.
Subtract from .
The exact value of is .
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.
To write as a fraction with a common denominator, multiply by .
Combine fractions.
Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
Multiply by .
Subtract from .
The exact value of is .
Find the point at .
Replace the variable with in the expression.
Simplify the result.
Subtract from .
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.
The exact value of is .
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.
To write as a fraction with a common denominator, multiply by .
Combine fractions.
Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
Multiply by .
Subtract from .
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.
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Subtract from .
Subtract full rotations of until the angle is greater than or equal to and less than .
The exact value of is .
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 fifty-two million seven hundred twelve thousand eight hundred seventy-eight

### Interesting facts

• 1952712878 has 16 divisors, whose sum is 3182691840
• The reverse of 1952712878 is 8782172591
• Previous prime number is 31

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 50
• Digital Root 5

### Name

Name four hundred eighty-five million four hundred forty-seven thousand two hundred twelve

### Interesting facts

• 485447212 has 8 divisors, whose sum is 1092256236
• The reverse of 485447212 is 212744584
• Previous prime number is 2

### Basic properties

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

### Name

Name seven hundred seventy-four million two hundred eighty-seven thousand six hundred seventy-nine

### Interesting facts

• 774287679 has 8 divisors, whose sum is 1126236672
• The reverse of 774287679 is 976782477
• Previous prime number is 11

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 9
• Sum of Digits 57
• Digital Root 3