Solve for x sin(x)=-0.78

$\sin (x) = - 0.78$

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

$x = \arcsin (- 0.78)$

Evaluate $\arcsin (- 0.78)$ .

$x = - 0.89466581$

The sine function is negative in the third and fourth quadrants. To find the second solution, subtract the solution from $2 π$ , to find a reference angle. Next, add this reference angle to $π$ to find the solution in the third quadrant.

$x = 2 (3.14159265) + 0.89466581 + 3.14159265$

Simplify the expression to find the second solution.

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Remove the parentheses around the expression $3.14159265$ .

$x = 2 (3.14159265) + 0.89466581 + 3.14159265$

Simplify $2 (3.14159265) + 0.89466581 + 3.14159265$ .

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Multiply $2$ by $3.14159265$ .

$x = 6.2831853 + 0.89466581 + 3.14159265$

Add $6.2831853$ and $0.89466581$ .

$x = 7.17785112 + 3.14159265$

Add $7.17785112$ and $3.14159265$ .

$x = 10.31944377$

Find the period.

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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.

$\frac{2 π}{| 1 |}$

Solve the equation.

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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 $1$ .

$2 π$

Add $2 π$ to every negative angle to get positive angles.

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Add $2 π$ to $- 0.89466581$ to find the positive angle.

$- 0.89466581 + 2 π$

Subtract $0.89466581$ from $2 π$ .

$5.38851948$

List the new angles.

$x = 5.38851948$

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

$x = 5.38851948 + 2 π n, 10.31944377 + 2 π n$ , for any integer $n$

Solve for x sin(x)=-0.78

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