Solve for θ in Degrees 8tan(theta)-12=5tan(theta)-9

Solve for θ in Degrees 8tan(theta)-12=5tan(theta)-9
Move all terms containing to the left side of the equation.
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Subtract from both sides of the equation.
Subtract from .
Move all terms not containing to the right side of the equation.
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Add to both sides of the equation.
Add and .
Divide each term in by and simplify.
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Divide each term in by .
Simplify the left side.
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Cancel the common factor of .
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Cancel the common factor.
Divide by .
Simplify the right side.
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Divide by .
Take the inverse tangent of both sides of the equation to extract from inside the tangent.
Simplify the right side.
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The exact value of is .
The tangent function is positive in the first and third quadrants. To find the second solution, subtract the reference angle from to find the solution in the fourth quadrant.
Add and .
Find the period of .
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The period of the function can be calculated using .
Replace with in the formula for period.
The absolute value is the distance between a number and zero. The distance between and is .
Divide by .
The period of the function is so values will repeat every degrees in both directions.
, for any integer
Consolidate the answers.
, for any integer
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Name

Name one billion fifty-one million one hundred forty-five thousand three hundred seven

Interesting facts

  • 1051145307 has 4 divisors, whose sum is 1167939240
  • The reverse of 1051145307 is 7035411501
  • Previous prime number is 9

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 27
  • Digital Root 9

Name

Name one hundred eighty-eight million two hundred twelve thousand five hundred fifty

Interesting facts

  • 188212550 has 16 divisors, whose sum is 300776112
  • The reverse of 188212550 is 055212881
  • Previous prime number is 41

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 32
  • Digital Root 5

Name

Name six hundred sixty-eight million thirty-nine thousand five hundred forty-six

Interesting facts

  • 668039546 has 8 divisors, whose sum is 1002287520
  • The reverse of 668039546 is 645930866
  • Previous prime number is 4679

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 47
  • Digital Root 2