Trigonometry Examples

$y = \frac{1}{2} \cdot \sin (x - \frac{π}{4})$

Step 1

Rewrite the equation as $\frac{1}{2} \cdot \sin (x - \frac{π}{4}) = y$ .

$\frac{1}{2} \cdot \sin (x - \frac{π}{4}) = y$

Step 2

Multiply both sides of the equation by $2$ .

$2 (\frac{1}{2} \sin (x - \frac{π}{4})) = 2 y$

Step 3

Simplify the left side.

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Step 3.1

Simplify $2 (\frac{1}{2} \sin (x - \frac{π}{4}))$ .

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Step 3.1.1

Combine $\frac{1}{2}$ and $\sin (x - \frac{π}{4})$ .

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

Step 3.1.2

Cancel the common factor of $2$ .

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Step 3.1.2.1

Cancel the common factor.

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

Step 3.1.2.2

Rewrite the expression.

$\sin (x - \frac{π}{4}) = 2 y$

Step 4

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

$x - \frac{π}{4} = \arcsin (2 y)$

Step 5

Add $\frac{π}{4}$ to both sides of the equation.

$x = \arcsin (2 y) + \frac{π}{4}$