Trigonometry Examples

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

Step 1

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

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

Step 2

Factor each term.

Tap for more steps...

Step 2.1

Evaluate $\sin (126.5)$ .

$\frac{13.5}{\sin (c)} = \frac{17.2}{0.80385686}$

Step 2.2

Divide $17.2$ by $0.80385686$ .

$\frac{13.5}{\sin (c)} = 21.39684419$

Step 3

Find the LCD of the terms in the equation.

Tap for more steps...

Step 3.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$\sin (c), 1$

Step 3.2

The LCM of one and any expression is the expression.

$\sin (c)$

Step 4

Multiply each term in $\frac{13.5}{\sin (c)} = 21.39684419$ by $\sin (c)$ to eliminate the fractions.

Tap for more steps...

Step 4.1

Multiply each term in $\frac{13.5}{\sin (c)} = 21.39684419$ by $\sin (c)$ .

$\frac{13.5}{\sin (c)} \sin (c) = 21.39684419 \sin (c)$

Step 4.2

Simplify the left side.

Tap for more steps...

Step 4.2.1

Cancel the common factor of $\sin (c)$ .

Tap for more steps...

Step 4.2.1.1

Cancel the common factor.

$\frac{13.5}{\sin (c)} \sin (c) = 21.39684419 \sin (c)$

Step 4.2.1.2

Rewrite the expression.

$13.5 = 21.39684419 \sin (c)$

Step 5

Solve the equation.

Tap for more steps...

Step 5.1

Rewrite the equation as $21.39684419 \sin (c) = 13.5$ .

$21.39684419 \sin (c) = 13.5$

Step 5.2

Divide each term in $21.39684419 \sin (c) = 13.5$ by $21.39684419$ and simplify.

Tap for more steps...

Step 5.2.1

Divide each term in $21.39684419 \sin (c) = 13.5$ by $21.39684419$ .

$\frac{21.39684419 \sin (c)}{21.39684419} = \frac{13.5}{21.39684419}$

Step 5.2.2

Simplify the left side.

Tap for more steps...

Step 5.2.2.1

Cancel the common factor of $21.39684419$ .

Tap for more steps...

Step 5.2.2.1.1

Cancel the common factor.

$\frac{21.39684419 \sin (c)}{21.39684419} = \frac{13.5}{21.39684419}$

Step 5.2.2.1.2

Divide $\sin (c)$ by $1$ .

$\sin (c) = \frac{13.5}{21.39684419}$

Step 5.2.3

Simplify the right side.

Tap for more steps...

Step 5.2.3.1

Divide $13.5$ by $21.39684419$ .

$\sin (c) = 0.63093416$

Step 6

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

$c = \arcsin (0.63093416)$

Step 7

Simplify the right side.

Tap for more steps...

Step 7.1

Evaluate $\arcsin (0.63093416)$ .

$c = 39.11907712$

Step 8

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 9

Subtract $39.11907712$ from $180$ .

$c = 140.88092287$

Step 10

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

Tap for more steps...

Step 10.1

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

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

Step 10.2

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

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

Step 10.3

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

$\frac{360}{1}$

Step 10.4

Divide $360$ by $1$ .

$360$

Step 11

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 $n$