Find the Exact Value tan(arccos(-15/17))

Find the Exact Value tan(arccos(-15/17))
Draw a triangle in the plane with vertices , , and the origin. Then is the angle between the positive x-axis and the ray beginning at the origin and passing through . Therefore, is .
Multiply the numerator by the reciprocal of the denominator.
One to any power is one.
Use the power rule to distribute the exponent.
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Apply the product rule to .
Apply the product rule to .
Multiply by by adding the exponents.
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Move .
Multiply by .
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Raise to the power of .
Use the power rule to combine exponents.
Add and .
Raise to the power of .
Raise to the power of .
Raise to the power of .
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.
Simplify the numerator.
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Multiply by .
Subtract from .
Rewrite as .
Simplify the numerator.
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Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
Simplify the denominator.
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Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
Simplify terms.
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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.
Combine and .
Simplify the expression.
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Multiply by .
Move the negative in front of the fraction.
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
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Name

Name one hundred thirty-six million nine hundred fifty thousand two hundred fifty-four

Interesting facts

  • 136950254 has 16 divisors, whose sum is 235032576
  • The reverse of 136950254 is 452059631
  • Previous prime number is 9871

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 35
  • Digital Root 8

Name

Name one billion nine hundred twenty-two million six hundred ten thousand seven hundred fifteen

Interesting facts

  • 1922610715 has 4 divisors, whose sum is 2307132864
  • The reverse of 1922610715 is 5170162291
  • Previous prime number is 5

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 34
  • Digital Root 7

Name

Name one billion sixty-seven million eight hundred seventy-three thousand nine hundred fifty-four

Interesting facts

  • 1067873954 has 32 divisors, whose sum is 1681838400
  • The reverse of 1067873954 is 4593787601
  • Previous prime number is 211

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 50
  • Digital Root 5