# Graph y=-3/2-cos(x)

Graph y=-3/2-cos(x)
Rewrite the expression as .
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 .
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.
The exact value of is .
Multiply by .
To write as a fraction with a common denominator, multiply by .
Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
Multiply by .
Subtract from .
Move the negative in front of the fraction.
The final answer is .
Find the point at .
Replace the variable with in the expression.
Simplify the result.
Simplify each term.
The exact value of is .
Multiply by .
Add and .
The final answer is .
Find the point at .
Replace the variable with in the expression.
Simplify the result.
Simplify each term.
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 .
Simplify the expression.
Write as a fraction with a common denominator.
Combine the numerators over the common denominator.
Add and .
Move the negative in front of the fraction.
The final answer is .
Find the point at .
Replace the variable with in the expression.
Simplify the result.
Simplify each term.
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.
The exact value of is .
Multiply by .
Add and .
The final answer is .
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 .
Multiply by .
To write as a fraction with a common denominator, multiply by .
Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
Multiply by .
Subtract from .
Move the negative in front of the fraction.
The final answer is .
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 four hundred eighty-eight million two hundred thirty-seven thousand ninety-six

### Interesting facts

• 488237096 has 16 divisors, whose sum is 1647800226
• The reverse of 488237096 is 690732884
• Previous prime number is 2

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 47
• Digital Root 2

### Name

Name one billion three hundred seventy-eight million seventy-four thousand twenty-four

### Interesting facts

• 1378074024 has 128 divisors, whose sum is 8299072512
• The reverse of 1378074024 is 4204708731
• Previous prime number is 271

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 36
• Digital Root 9

### Name

Name four hundred sixty-two million three hundred fourteen thousand four hundred twenty-eight

### Interesting facts

• 462314428 has 16 divisors, whose sum is 1041831000
• The reverse of 462314428 is 824413264
• Previous prime number is 643

### Basic properties

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