# Solve for x sin(2x)=( square root of 3)/2

Solve for x sin(2x)=( square root of 3)/2
Take the inverse sine of both sides of the equation to extract from inside the sine.
The exact value of is .
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Multiply .
Multiply and .
Multiply by .
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.
Simplify the expression to find the second solution.
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.
Subtract from .
Reorder and .
Subtract from .
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Simplify .
Multiply the numerator by the reciprocal of the denominator.
Cancel the common factor of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
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 .
Cancel the common factor of .
Cancel the common factor.
Divide by .
The period of the function is so values will repeat every radians in both directions.
, for any integer
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### Name

Name one billion three hundred seventy million five hundred thirty-seven thousand seven hundred fifty-two

### Interesting facts

• 1370537752 has 32 divisors, whose sum is 4701395520
• The reverse of 1370537752 is 2577350731
• Previous prime number is 61

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 40
• Digital Root 4

### Name

Name four hundred sixty-six million eighty-eight thousand seven hundred twelve

### Interesting facts

• 466088712 has 64 divisors, whose sum is 2098501344
• The reverse of 466088712 is 217880664
• Previous prime number is 2531

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 42
• Digital Root 6

### Name

Name two hundred seventy-five million six hundred twenty-four thousand two hundred eighteen

### Interesting facts

• 275624218 has 8 divisors, whose sum is 413809812
• The reverse of 275624218 is 812426572
• Previous prime number is 1117

### Basic properties

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