# 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 forty-seven million five hundred thirty-one thousand two hundred ninety

### Interesting facts

• 1547531290 has 32 divisors, whose sum is 2938187664
• The reverse of 1547531290 is 0921357451
• Previous prime number is 37

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 37
• Digital Root 1

### Name

Name eight hundred forty-eight million nine hundred sixty-five thousand nine hundred fifty-seven

### Interesting facts

• 848965957 has 8 divisors, whose sum is 983912832
• The reverse of 848965957 is 759569848
• Previous prime number is 71

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 9
• Sum of Digits 61
• Digital Root 7

### Name

Name eight hundred two million three hundred ninety-one thousand one hundred seventy-three

### Interesting facts

• 802391173 has 4 divisors, whose sum is 802459008
• The reverse of 802391173 is 371193208
• Previous prime number is 15263

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 9
• Sum of Digits 34
• Digital Root 7