Trigonometry Examples

$y = 3 \tan (2 x - 1)$

Step 1

Rewrite the equation as $3 \tan (2 x - 1) = y$ .

$3 \tan (2 x - 1) = y$

Step 2

Divide each term in $3 \tan (2 x - 1) = y$ by $3$ and simplify.

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Step 2.1

Divide each term in $3 \tan (2 x - 1) = y$ by $3$ .

$\frac{3 \tan (2 x - 1)}{3} = \frac{y}{3}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $3$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{3 \tan (2 x - 1)}{3} = \frac{y}{3}$

Step 2.2.1.2

Divide $\tan (2 x - 1)$ by $1$ .

$\tan (2 x - 1) = \frac{y}{3}$

Step 3

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

$2 x - 1 = \arctan (\frac{y}{3})$

Step 4

Add $1$ to both sides of the equation.

$2 x = \arctan (\frac{y}{3}) + 1$

Step 5

Divide each term in $2 x = \arctan (\frac{y}{3}) + 1$ by $2$ and simplify.

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Step 5.1

Divide each term in $2 x = \arctan (\frac{y}{3}) + 1$ by $2$ .

$\frac{2 x}{2} = \frac{\arctan (\frac{y}{3})}{2} + \frac{1}{2}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $2$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{\arctan (\frac{y}{3})}{2} + \frac{1}{2}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{\arctan (\frac{y}{3})}{2} + \frac{1}{2}$