Trigonometry Examples

$y = \sin (2 x - π)$

Step 1

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

$\sin (2 x - π) = y$

Step 2

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

$2 x - π = \arcsin (y)$

Step 3

Add $π$ to both sides of the equation.

$2 x = \arcsin (y) + π$

Step 4

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

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Step 4.1

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

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

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $2$ .

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Step 4.2.1.1

Cancel the common factor.

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

Step 4.2.1.2

Divide $x$ by $1$ .

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