Trigonometry Examples

$\sin (b) = \frac{9.86 \sin (31.6)}{22.45}$

Step 1

Simplify $\frac{9.86 \sin (31.6)}{22.45}$ .

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Step 1.1

Multiply $9.86$ by $\sin (31.6)$ .

$\sin (b) = \frac{5.16650103}{22.45}$

Step 1.2

Divide $5.16650103$ by $22.45$ .

$\sin (b) = 0.23013367$

Step 2

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

$b = \arcsin (0.23013367)$

Step 3

Simplify the right side.

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Step 3.1

Evaluate $\arcsin (0.23013367)$ .

$b = 13.30494195$

Step 4

The sine function is positive in the first and second quadrants. To find the second solution, subtract the reference angle from $180$ to find the solution in the second quadrant.

$b = 180 - 13.30494195$

Step 5

Subtract $13.30494195$ from $180$ .

$b = 166.69505804$

Step 6

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

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Step 6.1

The period of the function can be calculated using $\frac{360}{| b |}$ .

$\frac{360}{| b |}$

Step 6.2

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

$\frac{360}{| 1 |}$

Step 6.3

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

$\frac{360}{1}$

Step 6.4

Divide $360$ by $1$ .

$360$

Step 7

The period of the $\sin (b)$ function is $360$ so values will repeat every $360$ degrees in both directions.

$b = 13.30494195 + 360 n, 166.69505804 + 360 n$ , for any integer $n$