# Solve for θ in Degrees 2sin(theta)^2-3sin(theta)+1=0

Solve for θ in Degrees 2sin(theta)^2-3sin(theta)+1=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 .
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 .
Set equal to .
Solve for .
Add to both sides of the equation.
Divide each term in by and simplify.
Divide each term in by .
Simplify the left side.
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.
Simplify the right side.
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 .
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 .
Set equal to .
Solve for .
Add to both sides of the equation.
Take the inverse sine of both sides of the equation to extract from inside the sine.
Simplify the right side.
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 .
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
The final solution is all the values that make true.
, for any integer
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### Name

Name two hundred thirty-two million three hundred twenty-seven thousand three hundred seventy-eight

### Interesting facts

• 232327378 has 8 divisors, whose sum is 348581772
• The reverse of 232327378 is 873723232
• Previous prime number is 4517

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 37
• Digital Root 1

### Name

Name eighty million six hundred nine thousand four hundred thirty

### Interesting facts

• 80609430 has 16 divisors, whose sum is 122603616
• The reverse of 80609430 is 03490608
• Previous prime number is 137

### Basic properties

• Is Prime? no
• Number parity even
• Number length 8
• Sum of Digits 30
• Digital Root 3

### Name

Name two hundred sixty-one million seven hundred nine thousand seven hundred three

### Interesting facts

• 261709703 has 8 divisors, whose sum is 267642096
• The reverse of 261709703 is 307907162
• Previous prime number is 61

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 9
• Sum of Digits 35
• Digital Root 8