Trigonometry Examples

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

Step 1

Rewrite the equation as $1 + \tan (\frac{1}{2} x) = y$ .

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

Step 2

Subtract $1$ from both sides of the equation.

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

Step 3

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

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

Step 4

Simplify the left side.

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Step 4.1

Combine $\frac{1}{2}$ and $x$ .

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

Step 5

Multiply both sides of the equation by $2$ .

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

Step 6

Simplify the left side.

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Step 6.1

Cancel the common factor of $2$ .

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Step 6.1.1

Cancel the common factor.

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

Step 6.1.2

Rewrite the expression.

$x = 2 \arctan (y - 1)$