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

Solve for θ in Degrees 4sin(theta)^2=3
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 square root of both sides of the equation to eliminate the exponent on the left side.
Simplify .
Rewrite as .
Simplify the denominator.
Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
The complete solution is the result of both the positive and negative portions of the solution.
First, use the positive value of the to find the first solution.
Next, use the negative value of the to find the second solution.
The complete solution is the result of both the positive and negative portions of the solution.
Set up each of the solutions to solve for .
Solve for in .
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
Solve for in .
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 negative in the third and fourth quadrants. To find the second solution, subtract the solution from , to find a reference angle. Next, add this reference angle to to find the solution in the third quadrant.
Simplify the expression to find the second solution.
Subtract from .
The resulting angle of is positive, less than , and coterminal with .
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 .
Add to every negative angle to get positive angles.
Add to to find the positive angle.
Subtract from .
List the new angles.
The period of the function is so values will repeat every degrees in both directions.
, for any integer
, for any integer
List all of the solutions.
, for any integer
Consolidate the solutions.
Consolidate and to .
, for any integer
Consolidate and to .
, for any integer
, for any integer
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### Name

Name three hundred eight million eight hundred ninety thousand forty

### Interesting facts

• 308890040 has 32 divisors, whose sum is 1251004824
• The reverse of 308890040 is 040098803
• Previous prime number is 5

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 32
• Digital Root 5

### Name

Name five hundred fifty-six million six hundred thirty-three thousand one hundred seventy-three

### Interesting facts

• 556633173 has 8 divisors, whose sum is 757968768
• The reverse of 556633173 is 371336655
• Previous prime number is 47

### Basic properties

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

### Name

Name one billion nine hundred ninety-five million one hundred forty-one thousand four hundred forty-three

### Interesting facts

• 1995141443 has 4 divisors, whose sum is 1995355008
• The reverse of 1995141443 is 3441415991
• Previous prime number is 9791

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 41
• Digital Root 5