Find the Trig Value tan(theta)=24/7 , 0<=theta<=pi/2

Find the Trig Value tan(theta)=24/7 , 0<=theta<=pi/2
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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 two hundred six million eight hundred twenty-six thousand nine hundred eighty-seven

Interesting facts

  • 206826987 has 16 divisors, whose sum is 279272448
  • The reverse of 206826987 is 789628602
  • Previous prime number is 1553

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 9
  • Sum of Digits 48
  • Digital Root 3

Name

Name one hundred fifty-four million one hundred thirty-six thousand six hundred sixty-eight

Interesting facts

  • 154136668 has 16 divisors, whose sum is 396351504
  • The reverse of 154136668 is 866631451
  • Previous prime number is 7

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 40
  • Digital Root 4

Name

Name one billion two hundred eighty million one hundred ninety-four thousand sixty

Interesting facts

  • 1280194060 has 32 divisors, whose sum is 3461696352
  • The reverse of 1280194060 is 0604910821
  • Previous prime number is 673

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 31
  • Digital Root 4