Graph y=-3cos(x)

Graph y=-3cos(x)
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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The exact value of is .
Multiply by .
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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The exact value of is .
Multiply by .
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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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 .
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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Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.
The exact value of is .
Multiply by .
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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Subtract full rotations of until the angle is greater than or equal to and less than .
The exact value of is .
Multiply by .
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 eighty million seven hundred ninety-nine thousand five hundred seventy-eight

Interesting facts

  • 580799578 has 16 divisors, whose sum is 876308544
  • The reverse of 580799578 is 875997085
  • Previous prime number is 347

Basic properties

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

Name

Name six hundred ten million four hundred twenty-six thousand five hundred ninety-nine

Interesting facts

  • 610426599 has 16 divisors, whose sum is 646255584
  • The reverse of 610426599 is 995624016
  • Previous prime number is 53

Basic properties

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

Name

Name one billion four hundred twenty-four million three hundred eleven thousand four hundred twenty-five

Interesting facts

  • 1424311425 has 16 divisors, whose sum is 1626520896
  • The reverse of 1424311425 is 5241134241
  • Previous prime number is 17

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 27
  • Digital Root 9