# Graph y=2cos(x-pi/2)-1

Graph y=2cos(x-pi/2)-1
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.
Combine the numerators over the common denominator.
Subtract from .
Divide by .
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.
To write as a fraction with a common denominator, multiply by .
Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
Move to the left of .
Subtract from .
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.
Combine the numerators over the common denominator.
Subtract from .
Cancel the common factor of .
Cancel the common factor.
Divide by .
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 .
Subtract from .
Find the point at .
Replace the variable with in the expression.
Simplify the result.
Simplify each term.
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 .
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.
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.
Combine the numerators over the common denominator.
Subtract from .
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Divide by .
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 .
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 nine hundred ninety-two million seven hundred sixty-two thousand nine hundred forty-seven

### Interesting facts

• 992762947 has 8 divisors, whose sum is 1112285232
• The reverse of 992762947 is 749267299
• Previous prime number is 11

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 9
• Sum of Digits 55
• Digital Root 1

### Name

Name one billion one hundred fifty-four million two hundred forty-seven thousand two hundred thirty-five

### Interesting facts

• 1154247235 has 4 divisors, whose sum is 1385096688
• The reverse of 1154247235 is 5327424511
• Previous prime number is 5

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 34
• Digital Root 7

### Name

Name six hundred ninety-three million eight hundred eighty-eight thousand seven hundred forty-five

### Interesting facts

• 693888745 has 16 divisors, whose sum is 961797888
• The reverse of 693888745 is 547888396
• Previous prime number is 5

### Basic properties

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