Trigonometry Examples

$\frac{4.7}{9.9} = \sin (L)$

Step 1

Rewrite the equation as $\sin (L) = \frac{4.7}{9.9}$ .

$\sin (L) = \frac{4.7}{9.9}$

Step 2

Divide $4.7$ by $9.9$ .

$\sin (L) = 0.\overline{47}$

Step 3

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

$L = \arcsin (0.\overline{47})$

Step 4

Simplify the right side.

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Step 4.1

Evaluate $\arcsin (0.\overline{47})$ .

$L = 0.49467708$

Step 5

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.

$L = (3.14159265) - 0.49467708$

Step 6

Solve for $L$ .

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Step 6.1

Remove parentheses.

$L = 3.14159265 - 0.49467708$

Step 6.2

Remove parentheses.

$L = (3.14159265) - 0.49467708$

Step 6.3

Subtract $0.49467708$ from $3.14159265$ .

$L = 2.64691556$

Step 7

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

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Step 7.1

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

$\frac{2 π}{| b |}$

Step 7.2

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

$\frac{2 π}{| 1 |}$

Step 7.3

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

$\frac{2 π}{1}$

Step 7.4

Divide $2 π$ by $1$ .

$2 π$

Step 8

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

$L = 0.49467708 + 2 π n, 2.64691556 + 2 π n$ , for any integer $n$