Graph y=-2sin(3(x-pi/8))

Graph y=-2sin(3(x-pi/8))
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:
Multiply the numerator by the reciprocal of the denominator.
Phase Shift:
Cancel the common factor of .
Factor out of .
Phase Shift:
Cancel the common factor.
Phase Shift:
Rewrite the expression.
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.
Combine and .
Combine the numerators over the common denominator.
Subtract from .
Divide 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.
Combine the numerators over the common denominator.
Subtract from .
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
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 .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Combine the numerators over the common denominator.
Subtract from .
Cancel the common factor of .
Cancel the common factor.
Divide by .
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.
Multiply .
Combine and .
Multiply by .
Combine the numerators over the common denominator.
Subtract from .
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
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 .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Combine the numerators over the common denominator.
Subtract from .
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Divide by .
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 five hundred sixty-eight million sixty-four thousand ninety-nine

Interesting facts

• 1568064099 has 4 divisors, whose sum is 1642733840
• The reverse of 1568064099 is 9904608651
• Previous prime number is 21

Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 48
• Digital Root 3

Name

Name two hundred fifty-four million four hundred thousand five hundred eighty-one

Interesting facts

• 254400581 has 4 divisors, whose sum is 254697600
• The reverse of 254400581 is 185004452
• Previous prime number is 859

Basic properties

• Is Prime? no
• Number parity odd
• Number length 9
• Sum of Digits 29
• Digital Root 2

Name

Name two billion five million eight hundred forty-three thousand four hundred ten

Interesting facts

• 2005843410 has 32 divisors, whose sum is 3165520176
• The reverse of 2005843410 is 0143485002
• Previous prime number is 2333

Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 27
• Digital Root 9