Trigonometry Examples

$y = \sin (3 x + π)$

Step 1

Rewrite the equation as $\sin (3 x + π) = y$ .

$\sin (3 x + π) = y$

Step 2

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

$3 x + π = \arcsin (y)$

Step 3

Subtract $π$ from both sides of the equation.

$3 x = \arcsin (y) - π$

Step 4

Divide each term in $3 x = \arcsin (y) - π$ by $3$ and simplify.

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Step 4.1

Divide each term in $3 x = \arcsin (y) - π$ by $3$ .

$\frac{3 x}{3} = \frac{\arcsin (y)}{3} + \frac{- π}{3}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $3$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{\arcsin (y)}{3} + \frac{- π}{3}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{\arcsin (y)}{3} + \frac{- π}{3}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Move the negative in front of the fraction.

$x = \frac{\arcsin (y)}{3} - \frac{π}{3}$