# Graph y=2sin(3(x+pi/12))+4

Graph y=2sin(3(x+pi/12))+4
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:
Multiply .
Multiply and .
Phase Shift:
Multiply by .
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 left)
Vertical Shift:
Select a few points to graph.
Find the point at .
Replace the variable with in the expression.
Simplify the result.
Simplify each term.
Simplify each term.
Cancel the common factor of .
Move the leading negative in into the numerator.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Move the negative in front of the fraction.
Combine the numerators over the common denominator.
Divide by .
The exact value of is .
Multiply by .
Find the point at .
Replace the variable with in the expression.
Simplify the result.
Simplify each term.
Cancel the common factor of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Combine the numerators over the common denominator.
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.
Simplify each term.
Combine and .
Combine the numerators over the common denominator.
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.
Simplify each term.
Cancel the common factor of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Combine the numerators over the common denominator.
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.
Simplify each term.
Cancel the common factor of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Combine the numerators over the common denominator.
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 left)
Vertical Shift:
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### Name

Name one billion five hundred twenty-four million seven hundred forty-one thousand nine hundred twenty-one

### Interesting facts

• 1524741921 has 64 divisors, whose sum is 3778560000
• The reverse of 1524741921 is 1291474251
• Previous prime number is 599

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 36
• Digital Root 9

### Name

Name one billion two hundred million two hundred sixty thousand fifty-six

### Interesting facts

• 1200260056 has 32 divisors, whose sum is 4137067872
• The reverse of 1200260056 is 6500620021
• Previous prime number is 47

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 22
• Digital Root 4

### Name

Name three hundred sixty-six million three hundred eighty-six thousand seven hundred eighty-three

### Interesting facts

• 366386783 has 16 divisors, whose sum is 443741760
• The reverse of 366386783 is 387683663
• Previous prime number is 41

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 9
• Sum of Digits 50
• Digital Root 5