# Graph y=3cos(2x)

Graph y=3cos(2x)
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.
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. Make the expression negative because cosine is negative in the second 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 .
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.
The exact value of is .
Multiply by .
Find the point at .
Replace the variable with in the expression.
Simplify the result.
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 five hundred seventy-nine million six hundred eight thousand one hundred thirty-three

### Interesting facts

• 579608133 has 8 divisors, whose sum is 596946240
• The reverse of 579608133 is 331806975
• Previous prime number is 241

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 9
• Sum of Digits 42
• Digital Root 6

### Name

Name seven hundred twenty-eight million two hundred sixty-eight thousand eight hundred ninety-eight

### Interesting facts

• 728268898 has 32 divisors, whose sum is 1344752640
• The reverse of 728268898 is 898862827
• Previous prime number is 43

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 58
• Digital Root 4

### Name

Name seven hundred ten million six hundred nine thousand three hundred forty-three

### Interesting facts

• 710609343 has 4 divisors, whose sum is 947479128
• The reverse of 710609343 is 343906017
• Previous prime number is 3

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 9
• Sum of Digits 33
• Digital Root 6