Trigonometry Examples

$\arccos (x - \frac{1}{2}) = \frac{π}{3}$

Step 1

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

$x - \frac{1}{2} = \cos (\frac{π}{3})$

Step 2

Simplify the right side.

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Step 2.1

The exact value of $\cos (\frac{π}{3})$ is $\frac{1}{2}$ .

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

Step 3

Move all terms not containing $x$ to the right side of the equation.

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Step 3.1

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

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

Step 3.2

Combine the numerators over the common denominator.

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

Step 3.3

Add $1$ and $1$ .

$x = \frac{2}{2}$

Step 3.4

Divide $2$ by $2$ .

$x = 1$