Solve for x 4sin(x)^2+4sin(x)-3=0

Solve for x 4sin(x)^2+4sin(x)-3=0
Factor the left side of the equation.
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Let . Substitute for all occurrences of .
Factor by grouping.
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For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .
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Factor out of .
Rewrite as plus
Apply the distributive property.
Factor out the greatest common factor from each group.
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Group the first two terms and the last two terms.
Factor out the greatest common factor (GCF) from each group.
Factor the polynomial by factoring out the greatest common factor, .
Replace all occurrences of with .
Replace the left side with the factored expression.
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Set the first factor equal to and solve.
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Set the first factor equal to .
Add to both sides of the equation.
Divide each term by and simplify.
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Divide each term in by .
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Take the inverse sine of both sides of the equation to extract from inside the sine.
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.
Simplify .
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To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Combine.
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
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Move to the left of .
Subtract from .
Find the period.
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The period of the function can be calculated using .
Replace with in the formula for period.
Solve the equation.
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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 radians in both directions.
, for any integer
, for any integer
Set the next factor equal to and solve.
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Set the next factor equal to .
Subtract from both sides of the equation.
Divide each term by and simplify.
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Divide each term in by .
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Move the negative in front of the fraction.
The range of sine is . Since does not fall in this range, there is no solution.
No solution
No solution
The final solution is all the values that make true.
, for any integer
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Name

Name nine hundred sixty million four hundred thirty-seven thousand six hundred thirty-one

Interesting facts

  • 960437631 has 16 divisors, whose sum is 1025587200
  • The reverse of 960437631 is 136734069
  • Previous prime number is 479

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 9
  • Sum of Digits 39
  • Digital Root 3

Name

Name six hundred ten million four hundred fifty-four thousand nine hundred ninety-one

Interesting facts

  • 610454991 has 4 divisors, whose sum is 813939992
  • The reverse of 610454991 is 199454016
  • Previous prime number is 3

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 9
  • Sum of Digits 39
  • Digital Root 3

Name

Name eighty-one million nine hundred sixty-three thousand sixty-one

Interesting facts

  • 81963061 has 4 divisors, whose sum is 82039552
  • The reverse of 81963061 is 16036918
  • Previous prime number is 1087

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 8
  • Sum of Digits 34
  • Digital Root 7