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

Solve for x sin(x)=( square root of 2)/2
Take the inverse sine of both sides of the equation to extract from inside the sine.
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.
Simplify .
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.
Simplify the numerator.
Move to the left of .
Subtract from .
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 .
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 nine hundred six million five hundred eight thousand six hundred fifty-four

### Interesting facts

• 1906508654 has 16 divisors, whose sum is 2933990640
• The reverse of 1906508654 is 4568056091
• Previous prime number is 113

### Basic properties

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

### Name

Name one billion forty-two million one hundred sixteen thousand seven hundred seven

### Interesting facts

• 1042116707 has 4 divisors, whose sum is 1042345800
• The reverse of 1042116707 is 7076112401
• Previous prime number is 4643

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 29
• Digital Root 2

### Name

Name one billion nine hundred fourteen million six hundred twenty-four thousand nine hundred fifty-eight

### Interesting facts

• 1914624958 has 4 divisors, whose sum is 2871937440
• The reverse of 1914624958 is 8594264191
• Previous prime number is 2

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 49
• Digital Root 4