Solve for θ sin(theta)=0.4

$\sin (θ) = 0.4$

Step 1

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

$θ = \arcsin (0.4)$

Step 2

Simplify the right side.

Evaluate $\arcsin (0.4)$ .

$θ = 0.41151684$

Step 3

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.

$θ = (3.14159265) - 0.41151684$

Step 4

Solve for $θ$ .

Remove parentheses.

$θ = 3.14159265 - 0.41151684$

Remove parentheses.

$θ = (3.14159265) - 0.41151684$

Subtract $0.41151684$ from $3.14159265$ .

$θ = 2.7300758$

Step 5

Find the period of $\sin (θ)$ .

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 6

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

$θ = 0.41151684 + 2 π n, 2.7300758 + 2 π n$ , for any integer $n$

Solve for θ sin(theta)=0.4

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