Trigonometry Examples

$y = - 2 \sec (2 x + π)$

Step 1

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

$- 2 \sec (2 x + π) = y$

Step 2

Divide each term in $- 2 \sec (2 x + π) = y$ by $- 2$ and simplify.

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Step 2.1

Divide each term in $- 2 \sec (2 x + π) = y$ by $- 2$ .

$\frac{- 2 \sec (2 x + π)}{- 2} = \frac{y}{- 2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $- 2$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{- 2 \sec (2 x + π)}{- 2} = \frac{y}{- 2}$

Step 2.2.1.2

Divide $\sec (2 x + π)$ by $1$ .

$\sec (2 x + π) = \frac{y}{- 2}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Move the negative in front of the fraction.

$\sec (2 x + π) = - \frac{y}{2}$

Step 3

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

$2 x + π = arcsec (- \frac{y}{2})$

Step 4

Subtract $π$ from both sides of the equation.

$2 x = arcsec (- \frac{y}{2}) - π$

Step 5

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

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Step 5.1

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

$\frac{2 x}{2} = \frac{arcsec (- \frac{y}{2})}{2} + \frac{- π}{2}$

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.

$\frac{2 x}{2} = \frac{arcsec (- \frac{y}{2})}{2} + \frac{- π}{2}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{arcsec (- \frac{y}{2})}{2} + \frac{- π}{2}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Move the negative in front of the fraction.

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