Trigonometry Examples

$4 \arccos (5 x) = π$

Step 1

Divide each term in $4 \arccos (5 x) = π$ by $4$ and simplify.

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Step 1.1

Divide each term in $4 \arccos (5 x) = π$ by $4$ .

$\frac{4 \arccos (5 x)}{4} = \frac{π}{4}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $4$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{4 \arccos (5 x)}{4} = \frac{π}{4}$

Step 1.2.1.2

Divide $\arccos (5 x)$ by $1$ .

$\arccos (5 x) = \frac{π}{4}$

Step 2

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

$5 x = \cos (\frac{π}{4})$

Step 3

Simplify the right side.

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Step 3.1

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

$5 x = \frac{\sqrt{2}}{2}$

Step 4

Divide each term in $5 x = \frac{\sqrt{2}}{2}$ by $5$ and simplify.

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Step 4.1

Divide each term in $5 x = \frac{\sqrt{2}}{2}$ by $5$ .

$\frac{5 x}{5} = \frac{\frac{\sqrt{2}}{2}}{5}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $5$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{5 x}{5} = \frac{\frac{\sqrt{2}}{2}}{5}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{\frac{\sqrt{2}}{2}}{5}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Multiply the numerator by the reciprocal of the denominator.

$x = \frac{\sqrt{2}}{2} \cdot \frac{1}{5}$

Step 4.3.2

Multiply $\frac{\sqrt{2}}{2} \cdot \frac{1}{5}$ .

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Step 4.3.2.1

Multiply $\frac{\sqrt{2}}{2}$ by $\frac{1}{5}$ .

$x = \frac{\sqrt{2}}{2 \cdot 5}$

Step 4.3.2.2

Multiply $2$ by $5$ .

$x = \frac{\sqrt{2}}{10}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\sqrt{2}}{10}$

Decimal Form:

$x = 0.14142135 \dots$