# Solve for x in Radians sin(x)^2=3cos(x)^2

Solve for x in Radians sin(x)^2=3cos(x)^2
Subtract from both sides of the equation.
Replace the with based on the identity.
Subtract from .
Reorder the polynomial.
Subtract from 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 .
Simplify the right side.
Dividing two negative values results in a positive value.
Take the square root of both sides of the equation to eliminate the exponent on the left side.
Simplify .
Rewrite as .
Any root of is .
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 cosine of both sides of the equation to extract from inside the cosine.
Simplify the right side.
The exact value of is .
The cosine function is positive in the first and fourth quadrants. To find the second solution, subtract the reference angle from to find the solution in the fourth quadrant.
Simplify .
To write as a fraction with a common denominator, multiply by .
Combine fractions.
Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
Multiply by .
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 radians in both directions.
, for any integer
, for any integer
Solve for in .
Take the inverse cosine of both sides of the equation to extract from inside the cosine.
Simplify the right side.
The exact value of is .
The cosine function is negative in the second and third quadrants. To find the second solution, subtract the reference angle from to find the solution in the third quadrant.
Simplify .
To write as a fraction with a common denominator, multiply by .
Combine fractions.
Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
Multiply by .
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 radians 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 one billion one hundred twenty-two million eight hundred seventy thousand six hundred seventy-two

### Interesting facts

• 1122870672 has 512 divisors, whose sum is 7622657280
• The reverse of 1122870672 is 2760782211
• Previous prime number is 7

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 36
• Digital Root 9

### Name

Name seven hundred ninety-seven million eight hundred forty-six thousand three hundred ninety-three

### Interesting facts

• 797846393 has 4 divisors, whose sum is 798146448
• The reverse of 797846393 is 393648797
• Previous prime number is 2683

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 9
• Sum of Digits 56
• Digital Root 2

### Name

Name five hundred ninety-eight million two hundred eight thousand nine hundred forty-four

### Interesting facts

• 598208944 has 128 divisors, whose sum is 3095159040
• The reverse of 598208944 is 449802895
• Previous prime number is 191

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 49
• Digital Root 4