Solve for x in Degrees 2sin(x)tan(x)=9tan(x)

Solve for x in Degrees 2sin(x)tan(x)=9tan(x)
Subtract from both sides of the equation.
Factor out of .
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Factor out of .
Factor out of .
Factor out of .
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Set equal to and solve for .
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Set equal to .
Solve for .
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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
, for any integer
, for any integer
Set equal to and solve for .
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Set equal to .
Solve for .
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Add to both sides of the equation.
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 .
The range of sine is . Since does not fall in this range, there is no solution.
No solution
No solution
No solution
The final solution is all the values that make true.
, for any integer
Consolidate the answers.
, for any integer
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Name

Name one hundred forty-eight million four hundred fifty-eight thousand nine hundred forty-five

Interesting facts

  • 148458945 has 4 divisors, whose sum is 158356224
  • The reverse of 148458945 is 549854841
  • Previous prime number is 15

Basic properties

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

Name

Name four hundred two million one hundred ninety-eight thousand six hundred sixty-four

Interesting facts

  • 402198664 has 128 divisors, whose sum is 1789413120
  • The reverse of 402198664 is 466891204
  • Previous prime number is 109

Basic properties

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

Name

Name one billion four hundred eighty million six hundred thirty-three thousand one hundred eighty-four

Interesting facts

  • 1480633184 has 128 divisors, whose sum is 11254632480
  • The reverse of 1480633184 is 4813360841
  • Previous prime number is 1039

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 38
  • Digital Root 2