Find Trig Functions Using Identities tan(theta)=24/7 , sin(theta)>0

Find Trig Functions Using Identities tan(theta)=24/7 , sin(theta)>0
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The sine function is positive in the first and second quadrants. The tangent function is positive in the first and third quadrants. The set of solutions for are limited to the first quadrant since that is the only quadrant found in both sets.
Solution is in the first quadrant.
Use the definition of tangent 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
Raise to the power of .
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.
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 cotangent.
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Use the definition of cotangent to find the value of .
Substitute in the known values.
Find the value of secant.
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Use the definition of secant to find the value of .
Substitute in the known values.
Find the value of cosecant.
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Use the definition of cosecant to find the value of .
Substitute in the known values.
This is the solution to each trig value.
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Name

Name one billion eight hundred forty-seven million four hundred thirty-four thousand one hundred two

Interesting facts

  • 1847434102 has 4 divisors, whose sum is 2771151156
  • The reverse of 1847434102 is 2014347481
  • Previous prime number is 2

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 34
  • Digital Root 7

Name

Name two billion twenty-three million five hundred ninety-five thousand eight hundred forty-one

Interesting facts

  • 2023595841 has 8 divisors, whose sum is 2738398624
  • The reverse of 2023595841 is 1485953202
  • Previous prime number is 67

Basic properties

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

Name

Name one billion five hundred thirty-five million one hundred sixty-two thousand forty-five

Interesting facts

  • 1535162045 has 8 divisors, whose sum is 1842405720
  • The reverse of 1535162045 is 5402615351
  • Previous prime number is 15901

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 32
  • Digital Root 5