# Solve for x sin(x)=-1

Solve for x sin(x)=-1
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
, for any integer
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### Name

Name one billion five hundred forty-seven million four hundred fourteen thousand eight hundred fifty-six

### Interesting facts

• 1547414856 has 128 divisors, whose sum is 6394671360
• The reverse of 1547414856 is 6584147451
• Previous prime number is 43

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 45
• Digital Root 9

### Name

Name one billion three hundred fifty-four million eight hundred ninety-four thousand one hundred seventy-seven

### Interesting facts

• 1354894177 has 8 divisors, whose sum is 1667562176
• The reverse of 1354894177 is 7714984531
• Previous prime number is 7

### Basic properties

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

### Name

Name one billion five hundred fifty-eight million nine hundred fifty thousand five hundred eighty-two

### Interesting facts

• 1558950582 has 32 divisors, whose sum is 3201148800
• The reverse of 1558950582 is 2850598551
• Previous prime number is 163

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 48
• Digital Root 3