# Graph y=-3sin(1/2x)-1

Graph y=-3sin(1/2x)-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.
is approximately which is positive so remove the absolute value
Multiply the numerator by the reciprocal of the denominator.
Multiply 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:
Multiply 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.
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.
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 .
Cancel the common factor.
Divide by .
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.
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 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 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 two billion thirteen million nine hundred eighty-eight thousand four hundred twenty-six

### Interesting facts

• 2013988426 has 8 divisors, whose sum is 3021451524
• The reverse of 2013988426 is 6248893102
• Previous prime number is 6733

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 43
• Digital Root 7

### Name

Name five hundred seventy-five million six hundred fifty-seven thousand sixteen

### Interesting facts

• 575657016 has 256 divisors, whose sum is 3103930368
• The reverse of 575657016 is 610756575
• Previous prime number is 167

### Basic properties

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

### Name

Name one billion eight hundred seventy-nine million four hundred twenty-two thousand five hundred ten

### Interesting facts

• 1879422510 has 32 divisors, whose sum is 5154988032
• The reverse of 1879422510 is 0152249781
• Previous prime number is 3

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 39
• Digital Root 3