Trigonometry Examples

$y = 2 \sin (4 x + π)$

Step 1

Rewrite the equation as $2 \sin (4 x + π) = y$ .

$2 \sin (4 x + π) = y$

Step 2

Divide each term in $2 \sin (4 x + π) = y$ by $2$ and simplify.

Tap for more steps...

Step 2.1

Divide each term in $2 \sin (4 x + π) = y$ by $2$ .

$\frac{2 \sin (4 x + π)}{2} = \frac{y}{2}$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.2.1.1

Cancel the common factor.

$\frac{2 \sin (4 x + π)}{2} = \frac{y}{2}$

Step 2.2.1.2

Divide $\sin (4 x + π)$ by $1$ .

$\sin (4 x + π) = \frac{y}{2}$

Step 3

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

$4 x + π = \arcsin (\frac{y}{2})$

Step 4

Subtract $π$ from both sides of the equation.

$4 x = \arcsin (\frac{y}{2}) - π$

Step 5

Divide each term in $4 x = \arcsin (\frac{y}{2}) - π$ by $4$ and simplify.

Tap for more steps...

Step 5.1

Divide each term in $4 x = \arcsin (\frac{y}{2}) - π$ by $4$ .

$\frac{4 x}{4} = \frac{\arcsin (\frac{y}{2})}{4} + \frac{- π}{4}$

Step 5.2

Simplify the left side.

Tap for more steps...

Step 5.2.1

Cancel the common factor of $4$ .

Tap for more steps...

Step 5.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{\arcsin (\frac{y}{2})}{4} + \frac{- π}{4}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{\arcsin (\frac{y}{2})}{4} + \frac{- π}{4}$

Step 5.3

Simplify the right side.

Tap for more steps...

Step 5.3.1

Move the negative in front of the fraction.

$x = \frac{\arcsin (\frac{y}{2})}{4} - \frac{π}{4}$