Trigonometry Examples

$y = - 2 + 3 \tan (4 x + π)$

Step 1

Rewrite the equation as $- 2 + 3 \tan (4 x + π) = y$ .

$- 2 + 3 \tan (4 x + π) = y$

Step 2

Add $2$ to both sides of the equation.

$3 \tan (4 x + π) = y + 2$

Step 3

Divide each term in $3 \tan (4 x + π) = y + 2$ by $3$ and simplify.

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Step 3.1

Divide each term in $3 \tan (4 x + π) = y + 2$ by $3$ .

$\frac{3 \tan (4 x + π)}{3} = \frac{y}{3} + \frac{2}{3}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $3$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{3 \tan (4 x + π)}{3} = \frac{y}{3} + \frac{2}{3}$

Step 3.2.1.2

Divide $\tan (4 x + π)$ by $1$ .

$\tan (4 x + π) = \frac{y}{3} + \frac{2}{3}$

Step 4

Take the inverse tangent of both sides of the equation to extract $x$ from inside the tangent.

$4 x + π = \arctan (\frac{y}{3} + \frac{2}{3})$

Step 5

Subtract $π$ from both sides of the equation.

$4 x = \arctan (\frac{y}{3} + \frac{2}{3}) - π$

Step 6

Divide each term in $4 x = \arctan (\frac{y}{3} + \frac{2}{3}) - π$ by $4$ and simplify.

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Step 6.1

Divide each term in $4 x = \arctan (\frac{y}{3} + \frac{2}{3}) - π$ by $4$ .

$\frac{4 x}{4} = \frac{\arctan (\frac{y}{3} + \frac{2}{3})}{4} + \frac{- π}{4}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $4$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{\arctan (\frac{y}{3} + \frac{2}{3})}{4} + \frac{- π}{4}$

Step 6.2.1.2

Divide $x$ by $1$ .

$x = \frac{\arctan (\frac{y}{3} + \frac{2}{3})}{4} + \frac{- π}{4}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Move the negative in front of the fraction.

$x = \frac{\arctan (\frac{y}{3} + \frac{2}{3})}{4} - \frac{π}{4}$