# Solve for ? two sin(x) to the power of two minus three sin(x) plus one equals zero

Let . Substitute for all occurrences of .

Apply the grouping factorization.

For a polynomial of the form , Should be rewritten the middle term as a sum of two terms whose product is and whose sum is .

Factor out of .

Rewrite as plus

Use the distributive law.

Take the greatest common factor from each group out of the brackets.

Put together the Initially 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.

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, .

In case any individual factor in the left part of the equation equals , the entire expression will be equal to .

Set the first factor equal to .

Add to both sides of the equation.

Take the inverse sine of both sides of the equation to extract from inside the sine.

The exact value of is .

The 1st and 2nd quadrants of the sine function are positive. To calculate the second answer, subtract the reference angle from to find the solution in the second quadrant.

Clarify .

To write as a fraction with a common denominator, First, multiply by .

Write each expression with a common denominator of , by multiplying each by an appropriate factor of .

Add.

First, multiply by .

Add numerators over the common denominator.

Clarify the numerator.

Put to the left of .

Subtract from .

Calculate the period.

Evaluate the period of function using .

Replace with in the formula for period.

Find solution to the equation.

The absolute value is the distance between a number and zero. The distance between and is .

First, divide by .

The period of the function is so values will repeat every radians in two directions at once.

, for any integer

, for any integer

Set the Then factor equal to .

Add to both sides of the equation.

Divide each term by and simplify.

Divide each term in by .

The common factor should be canceled 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 calculate the second answer, 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

The final solution is all the values that make true.

, for any integer

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