Trigonometry Examples

$\frac{(13.5 \sin (126.5))}{17.2} = \sin (c)$

Step 1

Rewrite the equation as $\sin (c) = \frac{13.5 \sin (126.5)}{17.2}$ .

$\sin (c) = \frac{13.5 \sin (126.5)}{17.2}$

Step 2

Simplify $\frac{13.5 \sin (126.5)}{17.2}$ .

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Step 2.1

Multiply $13.5$ by $\sin (126.5)$ .

$\sin (c) = \frac{10.85206761}{17.2}$

Step 2.2

Divide $10.85206761$ by $17.2$ .

$\sin (c) = 0.63093416$

Step 3

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

$c = \arcsin (0.63093416)$

Step 4

Simplify the right side.

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Step 4.1

Evaluate $\arcsin (0.63093416)$ .

$c = 39.11907712$

Step 5

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.

$c = 180 - 39.11907712$

Step 6

Subtract $39.11907712$ from $180$ .

$c = 140.88092287$

Step 7

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

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Step 7.1

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

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

Step 7.2

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

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

Step 7.3

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

$\frac{360}{1}$

Step 7.4

Divide $360$ by $1$ .

$360$

Step 8

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

$c = 39.11907712 + 360 n, 140.88092287 + 360 n$ , for any integer $n$