Find the Other Trig Values in Quadrant II csc(theta) = square root of 2

Find the Other Trig Values in Quadrant II csc(theta) = square root of 2
Use the definition of cosecant to find the known sides of the unit circle right triangle. The quadrant determines the sign on each of the values.
Find the adjacent side of the unit circle triangle. Since the hypotenuse and opposite 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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Negate .
Adjacent
Rewrite as .
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Use to rewrite as .
Adjacent
Apply the power rule and multiply exponents, .
Adjacent
Combine and .
Adjacent
Cancel the common factor of .
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Cancel the common factor.
Adjacent
Rewrite the expression.
Adjacent
Adjacent
Evaluate the exponent.
Adjacent
Adjacent
One to any power is one.
Adjacent
Multiply by .
Adjacent
Subtract from .
Adjacent
Any root of is .
Adjacent
Multiply by .
Adjacent
Adjacent
Find the value of sine.
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Use the definition of sine 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 cosine.
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Use the definition of cosine 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 tangent.
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Use the definition of tangent to find the value of .
Substitute in the known values.
Divide by .
Find the value of cotangent.
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Use the definition of cotangent to find the value of .
Substitute in the known values.
Divide by .
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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Move the negative one from the denominator of .
Rewrite as .
This is the solution to each trig value.
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Name

Name one billion five hundred ninety-three million two hundred eighty-five thousand six hundred sixty-one

Interesting facts

  • 1593285661 has 8 divisors, whose sum is 1764072864
  • The reverse of 1593285661 is 1665823951
  • Previous prime number is 11

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 46
  • Digital Root 1

Name

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

Interesting facts

  • 36601336 has 16 divisors, whose sum is 123529536
  • The reverse of 36601336 is 63310663
  • Previous prime number is 2

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 8
  • Sum of Digits 28
  • Digital Root 1

Name

Name one billion eight hundred forty million six hundred eighty-three thousand two hundred ninety-eight

Interesting facts

  • 1840683298 has 16 divisors, whose sum is 2812512960
  • The reverse of 1840683298 is 8923860481
  • Previous prime number is 613

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 49
  • Digital Root 4