Trigonometry Examples

$y = - 2 \sin (2) (x - \frac{π}{6})$

Step 1

Rewrite the equation as $- 2 \sin (2) (x - \frac{π}{6}) = y$ .

$- 2 \sin (2) (x - \frac{π}{6}) = y$

Step 2

Simplify.

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Step 2.1

Evaluate $\sin (2)$ .

$- 2 \cdot 0.90929742 (x - \frac{π}{6}) = y$

Step 2.2

Multiply $- 2$ by $0.90929742$ .

$- 1.81859485 (x - \frac{π}{6}) = y$

Step 3

Divide each term in $- 1.81859485 (x - \frac{π}{6}) = y$ by $- 1.81859485$ and simplify.

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Step 3.1

Divide each term in $- 1.81859485 (x - \frac{π}{6}) = y$ by $- 1.81859485$ .

$\frac{- 1.81859485 (x - \frac{π}{6})}{- 1.81859485} = \frac{y}{- 1.81859485}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 1.81859485$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{- 1.81859485 (x - \frac{π}{6})}{- 1.81859485} = \frac{y}{- 1.81859485}$

Step 3.2.1.2

Divide $x - \frac{π}{6}$ by $1$ .

$x - \frac{π}{6} = \frac{y}{- 1.81859485}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Move the negative in front of the fraction.

$x - \frac{π}{6} = - \frac{y}{1.81859485}$

Step 3.3.2

Multiply by $1$ .

$x - \frac{π}{6} = - \frac{1 y}{1.81859485}$

Step 3.3.3

Factor $1.81859485$ out of $1.81859485$ .

$x - \frac{π}{6} = - \frac{1 y}{1.81859485 (1)}$

Step 3.3.4

Separate fractions.

$x - \frac{π}{6} = - (\frac{1}{1.81859485} \cdot \frac{y}{1})$

Step 3.3.5

Divide $1$ by $1.81859485$ .

$x - \frac{π}{6} = - (0.54987508 \frac{y}{1})$

Step 3.3.6

Divide $y$ by $1$ .

$x - \frac{π}{6} = - (0.54987508 y)$

Step 3.3.7

Multiply $0.54987508$ by $- 1$ .

$x - \frac{π}{6} = - 0.54987508 y$

Step 4

Add $\frac{π}{6}$ to both sides of the equation.

$x = - 0.54987508 y + \frac{π}{6}$