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

Solve for ? 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 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.
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.
Multiply by .
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 .
The resulting angle of is positive, less than , and coterminal with .
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 .
Add to every negative angle to get positive angles.
Add to to find the positive angle.
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.
Multiply by .
Subtract from .
List the new angles.
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 seven hundred eight million five hundred sixty-one thousand nine hundred sixteen

### Interesting facts

• 1708561916 has 8 divisors, whose sum is 3844264320
• The reverse of 1708561916 is 6191658071
• Previous prime number is 2

### Basic properties

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

### Name

Name four hundred eighty-eight million four hundred seventeen thousand six hundred twenty-seven

### Interesting facts

• 488417627 has 4 divisors, whose sum is 509653200
• The reverse of 488417627 is 726714884
• Previous prime number is 23

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 9
• Sum of Digits 47
• Digital Root 2

### Name

Name three hundred ninety-five million four hundred forty thousand four hundred sixty-one

### Interesting facts

• 395440461 has 8 divisors, whose sum is 398665600
• The reverse of 395440461 is 164044593
• Previous prime number is 151

### Basic properties

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