# Solve for θ in Degrees 3sin(theta)^2-4=-4sin(theta)

Solve for θ in Degrees 3sin(theta)^2-4=-4sin(theta)
Add to both sides of the equation.
Factor by grouping.
Reorder terms.
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, .
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.
Evaluate .
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 .
Subtract from both sides of the equation.
The range of sine is . Since does not fall in this range, there is no solution.
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 one hundred thirty-two million four hundred twenty-six thousand five hundred seventy-seven

### Interesting facts

• 132426577 has 4 divisors, whose sum is 132517476
• The reverse of 132426577 is 775624231
• Previous prime number is 1481

### Basic properties

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

### Name

Name three hundred eighty-seven million four hundred twenty-two thousand two hundred forty-one

### Interesting facts

• 387422241 has 8 divisors, whose sum is 523102080
• The reverse of 387422241 is 142224783
• Previous prime number is 79

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 9
• Sum of Digits 33
• Digital Root 6

### Name

Name one billion nine hundred ninety-eight million one hundred thousand seven hundred thirty-six

### Interesting facts

• 1998100736 has 512 divisors, whose sum is 51209143002
• The reverse of 1998100736 is 6370018991
• Previous prime number is 2

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 44
• Digital Root 8