Solve for x in Degrees tan(x)sin(x)+4sin(x)=0

Solve for x in Degrees tan(x)sin(x)+4sin(x)=0
Simplify the left side of the equation.
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Simplify each term.
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Rewrite in terms of sines and cosines.
Multiply .
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Combine and .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Add and .
Simplify each term.
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Factor out of .
Separate fractions.
Convert from to .
Divide by .
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 sine of both sides of the equation to extract from inside the sine.
Simplify the right side.
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The exact value of is .
The sine function is positive in the first and second quadrants. To find the second solution, subtract the reference angle from to find the solution in the second quadrant.
Subtract from .
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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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
The final solution is all the values that make true.
, for any integer
Consolidate the answers.
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Consolidate and to .
, for any integer
Consolidate and to .
, for any integer
, for any integer
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Name

Name eighty-eight million sixty-two thousand one hundred two

Interesting facts

  • 88062102 has 64 divisors, whose sum is 241470720
  • The reverse of 88062102 is 20126088
  • Previous prime number is 821

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 8
  • Sum of Digits 27
  • Digital Root 9

Name

Name two hundred twenty million nine hundred eighty thousand nine hundred eighty-eight

Interesting facts

  • 220980988 has 16 divisors, whose sum is 499044384
  • The reverse of 220980988 is 889089022
  • Previous prime number is 271

Basic properties

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

Name

Name one billion five hundred four million five hundred fifty-two thousand seven hundred forty-nine

Interesting facts

  • 1504552749 has 8 divisors, whose sum is 2292651840
  • The reverse of 1504552749 is 9472554051
  • Previous prime number is 3

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 42
  • Digital Root 6