Trigonometry Examples

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

Step 1

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

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

Step 2

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

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Step 2.1

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

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

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.

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

Step 2.2.1.2

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

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

Step 3

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

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

Step 4

Multiply both sides of the equation by $2$ .

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

Step 5

Simplify the left side.

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Step 5.1

Cancel the common factor of $2$ .

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Step 5.1.1

Cancel the common factor.

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

Step 5.1.2

Rewrite the expression.

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