Find the Other Trig Values in Quadrant I csc(theta)=2

Find the Other Trig Values in Quadrant I csc(theta)=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 .
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Raise to the power of .
Adjacent
One to any power is one.
Adjacent
Multiply by .
Adjacent
Subtract from .
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.
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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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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Rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Evaluate the exponent.
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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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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Rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Evaluate the exponent.
This is the solution to each trig value.
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Name

Name one billion two hundred nineteen million eight hundred seventy-four thousand one hundred seventy-three

Interesting facts

  • 1219874173 has 4 divisors, whose sum is 1394141920
  • The reverse of 1219874173 is 3714789121
  • Previous prime number is 7

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 43
  • Digital Root 7

Name

Name one billion two hundred fifty-four million two hundred fifty-nine thousand forty-eight

Interesting facts

  • 1254259048 has 128 divisors, whose sum is 4893872256
  • The reverse of 1254259048 is 8409524521
  • Previous prime number is 251

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 40
  • Digital Root 4

Name

Name one hundred twenty-five million seven hundred twenty-three thousand eight hundred twenty-five

Interesting facts

  • 125723825 has 32 divisors, whose sum is 187771392
  • The reverse of 125723825 is 528327521
  • Previous prime number is 67

Basic properties

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