Graph y=6sin(1/2x-8)+0

Graph y=6sin(1/2x-8)+0
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.
is approximately which is positive so remove the absolute value
Multiply the numerator by the reciprocal of the denominator.
Multiply 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:
Multiply the numerator by the reciprocal of the denominator.
Phase Shift:
Multiply 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.
Divide by .
Subtract from .
The exact value of is .
Multiply by .
The final answer is .
Find the point at .
Replace the variable with in the expression.
Simplify the result.
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 .
Add and .
The exact value of is .
Multiply by .
The final answer is .
Find the point at .
Replace the variable with in the expression.
Simplify the result.
Cancel the common factor of and .
Factor out of .
Factor out of .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Divide by .
Simplify by subtracting numbers.
Subtract from .
Add and .
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.
The exact value of is .
Multiply by .
The final answer is .
Find the point at .
Replace the variable with in the expression.
Simplify the result.
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 .
Add and .
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 .
The final answer is .
Find the point at .
Replace the variable with in the expression.
Simplify the result.
Cancel the common factor of and .
Factor out of .
Factor out of .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Divide by .
Simplify by subtracting numbers.
Subtract from .
Add and .
Subtract full rotations of until the angle is greater than or equal to and less than .
The exact value of is .
Multiply by .
The final answer 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 four hundred ninety-six million two hundred seventy-five thousand eight hundred twenty-two

Interesting facts

• 496275822 has 32 divisors, whose sum is 777093120
• The reverse of 496275822 is 228572694
• Previous prime number is 101

Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 45
• Digital Root 9

Name

Name thirty-five million six hundred eighty-eight thousand eight hundred seventy-five

Interesting facts

• 35688875 has 16 divisors, whose sum is 45388512
• The reverse of 35688875 is 57888653
• Previous prime number is 53

Basic properties

• Is Prime? no
• Number parity odd
• Number length 8
• Sum of Digits 50
• Digital Root 5

Name

Name eight hundred ninety-eight million one hundred forty-one thousand one hundred twenty-eight

Interesting facts

• 898141128 has 128 divisors, whose sum is 4080844800
• The reverse of 898141128 is 821141898
• Previous prime number is 199

Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 42
• Digital Root 6