Solve for x -sin(x)=-2/pi

$- \sin (x) = - \frac{2}{π}$

Step 1

Divide each term in $- \sin (x) = - \frac{2}{π}$ by $- 1$ and simplify.

Divide each term in $- \sin (x) = - \frac{2}{π}$ by $- 1$ .

$\frac{- \sin (x)}{- 1} = \frac{- \frac{2}{π}}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{\sin (x)}{1} = \frac{- \frac{2}{π}}{- 1}$

Divide $\sin (x)$ by $1$ .

$\sin (x) = \frac{- \frac{2}{π}}{- 1}$

Simplify the right side.

Dividing two negative values results in a positive value.

$\sin (x) = \frac{\frac{2}{π}}{1}$

Divide $\frac{2}{π}$ by $1$ .

$\sin (x) = \frac{2}{π}$

Step 2

Take the inverse sine of both sides of the equation to extract $x$ from inside the sine.

$x = \arcsin (\frac{2}{π})$

Step 3

Simplify the right side.

Evaluate $\arcsin (\frac{2}{π})$ .

$x = 0.69010709$

Step 4

The sine function is positive in the first and second quadrants. To find the second solution, subtract the reference angle from $π$ to find the solution in the second quadrant.

$x = (3.14159265) - 0.69010709$

Step 5

Solve for $x$ .

Remove parentheses.

$x = 3.14159265 - 0.69010709$

Remove parentheses.

$x = (3.14159265) - 0.69010709$

Subtract $0.69010709$ from $3.14159265$ .

$x = 2.45148556$

Step 6

Find the period of $\sin (x)$ .

The period of the function can be calculated using $\frac{2 π}{| b |}$ .

$\frac{2 π}{| b |}$

Replace $b$ with $1$ in the formula for period.

$\frac{2 π}{| 1 |}$

The absolute value is the distance between a number and zero. The distance between $0$ and $1$ is $1$ .

$\frac{2 π}{1}$

Divide $2 π$ by $1$ .

$2 π$

Step 7

The period of the $\sin (x)$ function is $2 π$ so values will repeat every $2 π$ radians in both directions.

$x = 0.69010709 + 2 π n, 2.45148556 + 2 π n$ , for any integer $n$

Solve for x -sin(x)=-2/pi

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