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 two hundred seventy-nine million one hundred eighty-eight thousand three hundred seventy-one

Interesting facts

  • 1279188371 has 8 divisors, whose sum is 1321014144
  • The reverse of 1279188371 is 1738819721
  • Previous prime number is 2797

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 47
  • Digital Root 2

Name

Name nine hundred eighty-eight million six hundred forty-nine thousand seven hundred ninety-nine

Interesting facts

  • 988649799 has 16 divisors, whose sum is 1361740800
  • The reverse of 988649799 is 997946889
  • Previous prime number is 1699

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 9
  • Sum of Digits 69
  • Digital Root 6

Name

Name four hundred nineteen million five hundred eighty-nine thousand fifty-four

Interesting facts

  • 419589054 has 16 divisors, whose sum is 1118904192
  • The reverse of 419589054 is 450985914
  • Previous prime number is 3

Basic properties

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