Trigonometry Examples

$4 \arccos (x) = π$

Step 1

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

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Step 1.1

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

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

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.

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

Step 1.2.1.2

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

$\arccos (x) = \frac{π}{4}$

Step 2

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

$x = \cos (\frac{π}{4})$

Step 3

Simplify the right side.

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Step 3.1

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

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 0.70710678 \dots$