Find the Other Trig Values in Quadrant IV cot(theta)=- square root of 3

Find the Other Trig Values in Quadrant IV cot(theta)=- square root of 3
Use the definition of cotangent to find the known sides of the unit circle right triangle. The quadrant determines the sign on each of the values.
Find the hypotenuse of the unit circle triangle. Since the opposite and adjacent sides are known, use the Pythagorean theorem to find the remaining side.
Replace the known values in the equation.
Simplify inside the radical.
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Raise to the power of .
Hypotenuse
Rewrite as .
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Use to rewrite as .
Hypotenuse
Apply the power rule and multiply exponents, .
Hypotenuse
Combine and .
Hypotenuse
Cancel the common factor of .
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Cancel the common factor.
Hypotenuse
Rewrite the expression.
Hypotenuse
Hypotenuse
Evaluate the exponent.
Hypotenuse
Hypotenuse
Add and .
Hypotenuse
Rewrite as .
Hypotenuse
Pull terms out from under the radical, assuming positive real numbers.
Hypotenuse
Hypotenuse
Find the value of sine.
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Use the definition of sine to find the value of .
Substitute in the known values.
Move the negative in front of the fraction.
Find the value of cosine.
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Use the definition of cosine to find the value of .
Substitute in the known values.
Find the value of tangent.
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Use the definition of tangent to find the value of .
Substitute in the known values.
Simplify the value of .
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Move the negative in front of the fraction.
Multiply by .
Combine and simplify the denominator.
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Multiply and .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Add and .
Rewrite as .
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Use to rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Evaluate the exponent.
Find the value of secant.
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Use the definition of secant to find the value of .
Substitute in the known values.
Simplify the value of .
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Multiply by .
Combine and simplify the denominator.
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Multiply and .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Add and .
Rewrite as .
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Use to rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Evaluate the exponent.
Find the value of cosecant.
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Use the definition of cosecant to find the value of .
Substitute in the known values.
Divide by .
This is the solution to each trig value.
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Name

Name six hundred three million thirty-seven thousand thirty-six

Interesting facts

  • 603037036 has 32 divisors, whose sum is 1551524832
  • The reverse of 603037036 is 630730306
  • Previous prime number is 2221

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 28
  • Digital Root 1

Name

Name one billion eight hundred twelve million one hundred six thousand five hundred ninety-six

Interesting facts

  • 1812106596 has 32 divisors, whose sum is 5437568160
  • The reverse of 1812106596 is 6956012181
  • Previous prime number is 5107

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 39
  • Digital Root 3

Name

Name one hundred fifteen million eight hundred forty thousand four hundred seventy-one

Interesting facts

  • 115840471 has 4 divisors, whose sum is 119835000
  • The reverse of 115840471 is 174048511
  • Previous prime number is 29

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 9
  • Sum of Digits 31
  • Digital Root 4