Find the Exact Value tan(112.5)

Find the Exact Value tan(112.5)
Rewrite as an angle where the values of the six trigonometric functions are known divided by .
Apply the tangent half-angle identity.
Change the to because tangent is negative in the second quadrant.
Simplify .
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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 third quadrant.
The exact value of is .
Multiply .
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Multiply by .
Multiply by .
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Combine.
Multiply by .
Combine the numerators over the common denominator.
Multiply 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 third quadrant.
The exact value of is .
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Combine.
Multiply by .
Combine the numerators over the common denominator.
Multiply by .
Multiply the numerator by the reciprocal of the denominator.
Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Multiply by .
Multiply and .
Expand the denominator using the FOIL method.
Simplify.
Apply the distributive property.
Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Combine and .
Simplify each term.
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Apply the distributive property.
Move to the left of .
Combine using the product rule for radicals.
Simplify each term.
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Multiply by .
Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
Cancel the common factor of and .
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Factor out of .
Factor out of .
Factor out of .
Cancel the common factors.
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Divide by .
Add and .
Add and .
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
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Name

Name eight hundred ten million three hundred thirty-two thousand nine hundred seventy-seven

Interesting facts

  • 810332977 has 8 divisors, whose sum is 813512000
  • The reverse of 810332977 is 779233018
  • Previous prime number is 1399

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 9
  • Sum of Digits 40
  • Digital Root 4

Name

Name one billion thirty-two million nine hundred sixty-four thousand three hundred forty-four

Interesting facts

  • 1032964344 has 64 divisors, whose sum is 3903221520
  • The reverse of 1032964344 is 4434692301
  • Previous prime number is 131

Basic properties

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

Name

Name one billion one hundred sixteen million five hundred thirty-six thousand sixty-eight

Interesting facts

  • 1116536068 has 16 divisors, whose sum is 2536597440
  • The reverse of 1116536068 is 8606356111
  • Previous prime number is 103

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 37
  • Digital Root 1