Solve for θ in Degrees tan(theta)^2+6tan(theta)+8=0

Solve for θ in Degrees tan(theta)^2+6tan(theta)+8=0
Factor the left side of the equation.
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Let . Substitute for all occurrences of .
Factor using the AC method.
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Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .
Write the factored form using these integers.
Replace all occurrences of with .
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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Subtract from both sides of the equation.
Take the inverse tangent of both sides of the equation to extract from inside the tangent.
Simplify the right side.
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Evaluate .
The tangent function is negative in the second and fourth quadrants. To find the second solution, subtract the reference angle from to find the solution in the third quadrant.
Simplify the expression to find the second solution.
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Add to .
The resulting angle of is positive and coterminal with .
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 .
Add to every negative angle to get positive angles.
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Add to to find the positive angle.
Subtract from .
List the new angles.
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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Subtract from both sides of the equation.
Take the inverse tangent of both sides of the equation to extract from inside the tangent.
Simplify the right side.
Tap for more steps...
Evaluate .
The tangent function is negative in the second and fourth quadrants. To find the second solution, subtract the reference angle from to find the solution in the third quadrant.
Simplify the expression to find the second solution.
Tap for more steps...
Add to .
The resulting angle of is positive and coterminal with .
Find the period of .
Tap for more steps...
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 .
Add to every negative angle to get positive angles.
Tap for more steps...
Add to to find the positive angle.
Subtract from .
List the new angles.
The period of the function is so values will repeat every degrees in both directions.
, for any integer
, for any integer
, for any integer
The final solution is all the values that make true.
, for any integer
Consolidate and to .
, for any integer
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Name

Name eight hundred nine million two hundred eighty-four thousand four hundred thirty-eight

Interesting facts

  • 809284438 has 8 divisors, whose sum is 1233827280
  • The reverse of 809284438 is 834482908
  • Previous prime number is 61

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 46
  • Digital Root 1

Name

Name fifty-four million two hundred two thousand one hundred sixteen

Interesting facts

  • 54202116 has 32 divisors, whose sum is 162891360
  • The reverse of 54202116 is 61120245
  • Previous prime number is 619

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 8
  • Sum of Digits 21
  • Digital Root 3

Name

Name five hundred eighty-eight million five hundred forty-four thousand four hundred fifty-eight

Interesting facts

  • 588544458 has 8 divisors, whose sum is 1177088928
  • The reverse of 588544458 is 854445885
  • Previous prime number is 3

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 51
  • Digital Root 6