# Graph y=10cos(pix-pi/2)

Graph y=10cos(pix-pi/2)
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.
is approximately which is positive so remove the absolute value
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:
Multiply the numerator by the reciprocal of the denominator.
Phase Shift:
Cancel the common factor of .
Cancel the common factor.
Phase Shift:
Rewrite the expression.
Phase Shift:
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.
Combine and .
Combine the numerators over the common denominator.
Subtract from .
Divide by .
The exact value of is .
Multiply by .
Find the point at .
Replace the variable with in the expression.
Simplify the result.
Multiply by .
To write as a fraction with a common denominator, multiply by .
Combine fractions.
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 .
Find the point at .
Replace the variable with in the expression.
Simplify the result.
Simplify each term.
Combine and .
Move to the left of .
Simplify terms.
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 .
Find the point at .
Replace the variable with in the expression.
Simplify the result.
Move to the left of .
To write as a fraction with a common denominator, multiply by .
Combine fractions.
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 .
Find the point at .
Replace the variable with in the expression.
Simplify the result.
Simplify each term.
Combine and .
Move to the left of .
Simplify terms.
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 .
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 twenty-nine million eight hundred seventy-seven thousand seven hundred fifty-five

### Interesting facts

• 529877755 has 16 divisors, whose sum is 642071808
• The reverse of 529877755 is 557778925
• 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 seventy-eight million four hundred ninety-eight thousand four hundred forty-three

### Interesting facts

• 78498443 has 4 divisors, whose sum is 78530808
• The reverse of 78498443 is 34489487
• Previous prime number is 2641

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 8
• Sum of Digits 47
• Digital Root 2

### Name

Name two billion eighty-five million nine hundred thirty-nine thousand eight hundred sixty-four

### Interesting facts

• 2085939864 has 128 divisors, whose sum is 9745505280
• The reverse of 2085939864 is 4689395802
• Previous prime number is 2237

### Basic properties

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