Trigonometry Examples

$y = 3 \sin (4) (x - \frac{π}{3})$

Step 1

Rewrite the equation as $3 \sin (4) (x - \frac{π}{3}) = y$ .

$3 \sin (4) (x - \frac{π}{3}) = y$

Step 2

Simplify.

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Step 2.1

Evaluate $\sin (4)$ .

$3 \cdot - 0.75680249 (x - \frac{π}{3}) = y$

Step 2.2

Multiply $3$ by $- 0.75680249$ .

$- 2.27040748 (x - \frac{π}{3}) = y$

Step 3

Divide each term in $- 2.27040748 (x - \frac{π}{3}) = y$ by $- 2.27040748$ and simplify.

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Step 3.1

Divide each term in $- 2.27040748 (x - \frac{π}{3}) = y$ by $- 2.27040748$ .

$\frac{- 2.27040748 (x - \frac{π}{3})}{- 2.27040748} = \frac{y}{- 2.27040748}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 2.27040748$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{- 2.27040748 (x - \frac{π}{3})}{- 2.27040748} = \frac{y}{- 2.27040748}$

Step 3.2.1.2

Divide $x - \frac{π}{3}$ by $1$ .

$x - \frac{π}{3} = \frac{y}{- 2.27040748}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Move the negative in front of the fraction.

$x - \frac{π}{3} = - \frac{y}{2.27040748}$

Step 3.3.2

Multiply by $1$ .

$x - \frac{π}{3} = - \frac{1 y}{2.27040748}$

Step 3.3.3

Factor $2.27040748$ out of $2.27040748$ .

$x - \frac{π}{3} = - \frac{1 y}{2.27040748 (1)}$

Step 3.3.4

Separate fractions.

$x - \frac{π}{3} = - (\frac{1}{2.27040748} \cdot \frac{y}{1})$

Step 3.3.5

Divide $1$ by $2.27040748$ .

$x - \frac{π}{3} = - (0.44044956 \frac{y}{1})$

Step 3.3.6

Divide $y$ by $1$ .

$x - \frac{π}{3} = - (0.44044956 y)$

Step 3.3.7

Multiply $0.44044956$ by $- 1$ .

$x - \frac{π}{3} = - 0.44044956 y$

Step 4

Add $\frac{π}{3}$ to both sides of the equation.

$x = - 0.44044956 y + \frac{π}{3}$