Trigonometry Examples

$\sin (315) = \frac{x}{12}$

Step 1

Rewrite the equation as $\frac{x}{12} = \sin (315)$ .

$\frac{x}{12} = \sin (315)$

Step 2

Multiply both sides of the equation by $12$ .

$12 \frac{x}{12} = 12 \sin (315)$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $12$ .

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Step 3.1.1.1

Cancel the common factor.

$12 \frac{x}{12} = 12 \sin (315)$

Step 3.1.1.2

Rewrite the expression.

$x = 12 \sin (315)$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $12 \sin (315)$ .

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Step 3.2.1.1

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because sine is negative in the fourth quadrant.

$x = 12 (- \sin (45))$

Step 3.2.1.2

The exact value of $\sin (45)$ is $\frac{\sqrt{2}}{2}$ .

$x = 12 (- \frac{\sqrt{2}}{2})$

Step 3.2.1.3

Cancel the common factor of $2$ .

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Step 3.2.1.3.1

Move the leading negative in $- \frac{\sqrt{2}}{2}$ into the numerator.

$x = 12 \frac{- \sqrt{2}}{2}$

Step 3.2.1.3.2

Factor $2$ out of $12$ .

$x = 2 (6) \frac{- \sqrt{2}}{2}$

Step 3.2.1.3.3

Cancel the common factor.

$x = 2 \cdot 6 \frac{- \sqrt{2}}{2}$

Step 3.2.1.3.4

Rewrite the expression.

$x = 6 (- \sqrt{2})$

Step 3.2.1.4

Multiply $- 1$ by $6$ .

$x = - 6 \sqrt{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = - 6 \sqrt{2}$

Decimal Form:

$x = - 8.48528137 \dots$