# 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 eight hundred fifty-five million two hundred eighty-one thousand eight hundred fifty-six

### Interesting facts

• 855281856 has 1024 divisors, whose sum is 15260990976
• The reverse of 855281856 is 658182558
• Previous prime number is 13

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 48
• Digital Root 3

### Name

Name one billion two hundred fourteen million seven hundred sixty-one thousand five hundred seventy-nine

### Interesting facts

• 1214761579 has 4 divisors, whose sum is 1216131984
• The reverse of 1214761579 is 9751674121
• Previous prime number is 887

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 43
• Digital Root 7

### Name

Name one billion four hundred sixty-two million five hundred forty-eight thousand nine hundred fifty-five

### Interesting facts

• 1462548955 has 8 divisors, whose sum is 1569742848
• The reverse of 1462548955 is 5598452641
• Previous prime number is 23

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 49
• Digital Root 4