Graph sin(2x)-sin(5x)

Graph sin(2x)-sin(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 .
Cancel the common factor of .
Cancel the common factor.
Divide 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:
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.
Simplify each term.
Multiply by .
The exact value of is .
Multiply 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.
The exact value of is .
Combine 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 third quadrant.
The exact value of is .
Multiply .
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 .
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 .
Combine and .
Subtract full rotations of until the angle is greater than or equal to and less than .
The exact value of is .
Multiply by .
Subtract from .
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.
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 .
Combine and .
Multiply by .
Subtract full rotations of until the angle is greater than or equal to and less than .
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 .
Multiply by .
Multiply by .
Find the point at .
Replace the variable with in the expression.
Simplify the result.
Simplify each term.
Subtract full rotations of until the angle is greater than or equal to and less than .
The exact value of is .
Subtract full rotations of until the angle is greater than or equal to and less than .
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.
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 one billion one hundred twenty-four million five hundred fifty-two thousand five hundred eighty-nine

Interesting facts

• 1124552589 has 16 divisors, whose sum is 1523478528
• The reverse of 1124552589 is 9852554211
• Previous prime number is 67

Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 42
• Digital Root 6

Name

Name one billion five hundred seventy-nine million forty-seven thousand eight hundred forty-nine

Interesting facts

• 1579047849 has 8 divisors, whose sum is 1755465000
• The reverse of 1579047849 is 9487409751
• Previous prime number is 1849

Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 54
• Digital Root 9

Name

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

Interesting facts

• 1609096496 has 256 divisors, whose sum is 8609781600
• The reverse of 1609096496 is 6946909061
• Previous prime number is 113

Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 50
• Digital Root 5