# Graph y=-6sin(5x)

Graph y=-6sin(5x)
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:
Divide 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.
Multiply 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.
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.
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.
Cancel the common factor of .
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 .
Cancel the common factor.
Rewrite the expression.
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 two hundred sixty-four million six hundred forty-two thousand fourteen

### Interesting facts

• 264642014 has 16 divisors, whose sum is 406183680
• The reverse of 264642014 is 410246462
• Previous prime number is 83

### Basic properties

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

### Name

Name one billion sixty-eight million seven hundred twenty thousand six hundred seven

### Interesting facts

• 1068720607 has 4 divisors, whose sum is 1124969080
• The reverse of 1068720607 is 7060278601
• Previous prime number is 19

### Basic properties

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

### Name

Name one billion six hundred one million nine hundred fifty-six thousand four hundred six

### Interesting facts

• 1601956406 has 4 divisors, whose sum is 2402934612
• The reverse of 1601956406 is 6046591061
• Previous prime number is 2

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 38
• Digital Root 2