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 .
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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 .
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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.
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Find the point at .
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Replace the variable with in the expression.
Simplify the result.
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Simplify each term.
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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.
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Multiply by .
Subtract from .
Move the negative in front of the fraction.
The final answer is .
Find the point at .
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Replace the variable with in the expression.
Simplify the result.
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Simplify each term.
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The exact value of is .
Multiply by .
Add and .
The final answer is .
Find the point at .
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Replace the variable with in the expression.
Simplify the result.
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Simplify each term.
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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.
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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 .
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Replace the variable with in the expression.
Simplify the result.
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Simplify each term.
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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 .
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Replace the variable with in the expression.
Simplify the result.
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Simplify each term.
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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.
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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 five hundred fifty-one million nine hundred eighty thousand three hundred forty-four

Interesting facts

  • 551980344 has 32 divisors, whose sum is 1899463176
  • The reverse of 551980344 is 443089155
  • Previous prime number is 51

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 39
  • Digital Root 3

Name

Name seven hundred ninety million seven hundred twenty-seven thousand four hundred eighty-four

Interesting facts

  • 790727484 has 64 divisors, whose sum is 2502783360
  • The reverse of 790727484 is 484727097
  • Previous prime number is 461

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 48
  • Digital Root 3

Name

Name one billion three hundred twenty-six million one hundred eighty-two thousand nine hundred thirteen

Interesting facts

  • 1326182913 has 4 divisors, whose sum is 1339578800
  • The reverse of 1326182913 is 3192816231
  • Previous prime number is 99

Basic properties

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