Trigonometry Examples

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

Step 1

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

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

Step 2

Simplify the right side.

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Step 2.1

The exact value of $\cos (\frac{π}{4})$ is $\frac{\sqrt{2}}{2}$ .

$x - \frac{1}{2} = \frac{\sqrt{2}}{2}$

Step 3

Add $\frac{1}{2}$ to both sides of the equation.

$x = \frac{\sqrt{2}}{2} + \frac{1}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\sqrt{2}}{2} + \frac{1}{2}$

Decimal Form:

$x = 1.20710678 \dots$