Trigonometry Examples

$y = - \tan (x - \frac{π}{2})$

Step 1

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

$- \tan (x - \frac{π}{2}) = y$

Step 2

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

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Step 2.1

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

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

Step 2.2

Simplify the left side.

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Step 2.2.1

Dividing two negative values results in a positive value.

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

Step 2.2.2

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

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

Step 2.3

Simplify the right side.

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Step 2.3.1

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

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

Step 2.3.2

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

$\tan (x - \frac{π}{2}) = - y$

Step 3

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

$x - \frac{π}{2} = \arctan (- y)$

Step 4

Add $\frac{π}{2}$ to both sides of the equation.

$x = \arctan (- y) + \frac{π}{2}$