Trigonometry Examples

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

Step 1

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

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

Step 2

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

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Step 2.1

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

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

Step 2.2

Simplify the left side.

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Step 2.2.1

Dividing two negative values results in a positive value.

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

Step 2.2.2

Divide $\tan (\frac{1}{2} x)$ by $1$ .

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

Step 2.3

Simplify the right side.

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Step 2.3.1

Move the negative one from the denominator of $\frac{y}{- 1}$ .

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

Step 2.3.2

Rewrite $- 1 \cdot y$ as $- y$ .

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

Step 3

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

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

Step 4

Simplify the left side.

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Step 4.1

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

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

Step 5

Multiply both sides of the equation by $2$ .

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

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.

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

Step 6.1.2

Rewrite the expression.

$x = 2 \arctan (- y)$