Trigonometry Examples

$13 \arccos (x) - 2 π = \arccos (x)$

Step 1

Move all terms containing $x$ to the left side of the equation.

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Step 1.1

Subtract $\arccos (x)$ from both sides of the equation.

$13 \arccos (x) - 2 π - \arccos (x) = 0$

Step 1.2

Subtract $\arccos (x)$ from $13 \arccos (x)$ .

$12 \arccos (x) - 2 π = 0$

Step 2

Add $2 π$ to both sides of the equation.

$12 \arccos (x) = 2 π$

Step 3

Divide each term in $12 \arccos (x) = 2 π$ by $12$ and simplify.

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Step 3.1

Divide each term in $12 \arccos (x) = 2 π$ by $12$ .

$\frac{12 \arccos (x)}{12} = \frac{2 π}{12}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $12$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{12 \arccos (x)}{12} = \frac{2 π}{12}$

Step 3.2.1.2

Divide $\arccos (x)$ by $1$ .

$\arccos (x) = \frac{2 π}{12}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Cancel the common factor of $2$ and $12$ .

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Step 3.3.1.1

Factor $2$ out of $2 π$ .

$\arccos (x) = \frac{2 (π)}{12}$

Step 3.3.1.2

Cancel the common factors.

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Step 3.3.1.2.1

Factor $2$ out of $12$ .

$\arccos (x) = \frac{2 π}{2 \cdot 6}$

Step 3.3.1.2.2

Cancel the common factor.

$\arccos (x) = \frac{2 π}{2 \cdot 6}$

Step 3.3.1.2.3

Rewrite the expression.

$\arccos (x) = \frac{π}{6}$

Step 4

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

$x = \cos (\frac{π}{6})$

Step 5

Simplify the right side.

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Step 5.1

The exact value of $\cos (\frac{π}{6})$ is $\frac{\sqrt{3}}{2}$ .

$x = \frac{\sqrt{3}}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\sqrt{3}}{2}$

Decimal Form:

$x = 0.86602540 \dots$