Find the Other Trig Values in Quadrant I sec(x)=12

Find the Other Trig Values in Quadrant I sec(x)=12
Use the definition of secant to find the known sides of the unit circle right triangle. The quadrant determines the sign on each of the values.
Find the opposite side of the unit circle triangle. Since the adjacent side and hypotenuse 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 .
Opposite
One to any power is one.
Opposite
Multiply by .
Opposite
Subtract from .
Opposite
Opposite
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.
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.
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 cosecant.
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Use the definition of cosecant 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 twenty-nine million five hundred thirty-two thousand six hundred twenty-nine

Interesting facts

  • 1229532629 has 16 divisors, whose sum is 1427242992
  • The reverse of 1229532629 is 9262359221
  • Previous prime number is 1433

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 41
  • Digital Root 5

Name

Name one billion one hundred twenty-three million six hundred eighty-two thousand eighty-four

Interesting facts

  • 1123682084 has 16 divisors, whose sum is 2889468288
  • The reverse of 1123682084 is 4802863211
  • Previous prime number is 7

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 35
  • Digital Root 8

Name

Name one hundred fifty-two million three hundred twenty-two thousand six hundred fourteen

Interesting facts

  • 152322614 has 4 divisors, whose sum is 228483924
  • The reverse of 152322614 is 416223251
  • Previous prime number is 2

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 26
  • Digital Root 8