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.
Let . Substitute for all occurrences of .
Factor by grouping.
For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .
Factor out of .
Rewrite as plus
Apply the distributive property.
Factor out the greatest common factor from each group.
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.
Set the first factor equal to .
Add to both sides of the equation.
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
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 .
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 .
Combine.
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
Move to the left of .
Subtract from .
Find the period.
The period of the function can be calculated using .
Replace with in the formula for period.
Solve the equation.
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.
Set the next factor equal to .
Subtract from both sides of the equation.
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
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