Evaluate sin(theta)=3/5

$\sin (θ) = \frac{3}{5}$

Step 1

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

$θ = \arcsin (\frac{3}{5})$

Step 2

Simplify the right side.

Evaluate $\arcsin (\frac{3}{5})$ .

$θ = 0.6435011$

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.

$θ = (3.14159265) - 0.6435011$

Step 4

Solve for $θ$ .

Remove parentheses.

$θ = 3.14159265 - 0.6435011$

Remove parentheses.

$θ = (3.14159265) - 0.6435011$

Subtract $0.6435011$ from $3.14159265$ .

$θ = 2.49809154$

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.

$θ = 0.6435011 + 2 π n, 2.49809154 + 2 π n$ , for any integer $n$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\sin (θ) = \frac{3}{5}$

Decimal Form:

$\sin (θ) = 0.6$

Evaluate sin(theta)=3/5

Related Questions

Support LCMGCF.com by disabling your adblocker.