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 eight hundred forty-three million four hundred nineteen thousand one hundred

Interesting facts

• 843419100 has 32 divisors, whose sum is 2631468528
• The reverse of 843419100 is 001914348
• Previous prime number is 3

Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 30
• Digital Root 3

Name

Name one billion ninety-six million six hundred twenty-one thousand three hundred eighty-six

Interesting facts

• 1096621386 has 64 divisors, whose sum is 2543063040
• The reverse of 1096621386 is 6831266901
• Previous prime number is 107

Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 42
• Digital Root 6

Name

Name three hundred forty-four million eight hundred fifty-three thousand nine hundred eleven

Interesting facts

• 344853911 has 4 divisors, whose sum is 353265024
• The reverse of 344853911 is 119358443
• Previous prime number is 41

Basic properties

• Is Prime? no
• Number parity odd
• Number length 9
• Sum of Digits 38
• Digital Root 2