# Solve for x sin(2x)=-1

Solve for x sin(2x)=-1
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 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.
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.
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.
Multiply by .
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 .
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 .
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.
Move to the left of .
Subtract from .
List the new angles.
The period of the function is so values will repeat every radians in both directions.
, for any integer
, for any integer
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### Name

Name two hundred sixty million fifty-three thousand eight hundred ninety-one

### Interesting facts

• 260053891 has 8 divisors, whose sum is 263343600
• The reverse of 260053891 is 198350062
• Previous prime number is 389

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 9
• Sum of Digits 34
• Digital Root 7

### Name

Name one billion one hundred forty-three million nine hundred thirty-one thousand eight hundred seventy-two

### Interesting facts

• 1143931872 has 256 divisors, whose sum is 11828788992
• The reverse of 1143931872 is 2781393411
• Previous prime number is 47

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 39
• Digital Root 3

### Name

Name six hundred thirty-eight million four hundred twenty-two thousand five

### Interesting facts

• 638422005 has 32 divisors, whose sum is 1184674176
• The reverse of 638422005 is 500224836
• Previous prime number is 13

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 9
• Sum of Digits 30
• Digital Root 3