Graph cos((2n+1)*90)

Graph cos((2n+1)*90)
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 .
Cancel the common factor of and .
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Factor out of .
Cancel the common factors.
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Factor out of .
Cancel the common factor.
Rewrite the expression.
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:
Cancel the common factor of and .
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Factor out of .
Phase Shift:
Cancel the common factors.
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Factor out of .
Phase Shift:
Cancel the common factor.
Phase Shift:
Rewrite the expression.
Phase Shift:
Phase Shift:
Phase Shift:
Move the negative in front of the fraction.
Phase Shift:
Phase Shift:
Find the vertical shift .
Vertical Shift:
List the properties of the trigonometric function.
Amplitude:
Period:
Phase Shift: ( to the left)
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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Cancel the common factor of .
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Move the leading negative in into the numerator.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Multiply by .
Add and .
The exact value of is .
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 distributive property.
Cancel the common factor of .
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
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Move the leading negative in into the numerator.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Multiply by .
Simplify by adding numbers.
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Add and .
Add and .
The exact value of is .
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 distributive property.
Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
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Move the leading negative in into the numerator.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Multiply by .
Simplify by adding numbers.
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Add and .
Add and .
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 .
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 distributive property.
Cancel the common factor of .
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Factor out of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Combine and .
Cancel the common factor of .
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Move the leading negative in into the numerator.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Multiply by .
Simplify by adding numbers.
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Add and .
Add and .
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.
The exact value of is .
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 distributive property.
Cancel the common factor of .
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
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Move the leading negative in into the numerator.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Multiply by .
Simplify by adding numbers.
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Add and .
Add and .
Subtract full rotations of until the angle is greater than or equal to and less than .
The exact value of is .
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 left)
Vertical Shift:
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Name

Name one billion seven hundred eight million eight hundred seventy-six thousand one hundred four

Interesting facts

  • 1708876104 has 128 divisors, whose sum is 8298702720
  • The reverse of 1708876104 is 4016788071
  • Previous prime number is 503

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 42
  • Digital Root 6

Name

Name eight hundred sixty-seven million one hundred sixteen thousand nine hundred forty-three

Interesting facts

  • 867116943 has 32 divisors, whose sum is 1073088000
  • The reverse of 867116943 is 349611768
  • Previous prime number is 89

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 9
  • Sum of Digits 45
  • Digital Root 9

Name

Name one billion nine hundred fifteen million six hundred eight thousand three hundred twenty-one

Interesting facts

  • 1915608321 has 8 divisors, whose sum is 1981058144
  • The reverse of 1915608321 is 1238065191
  • Previous prime number is 33

Basic properties

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