Trigonometry Examples

$6 \arccos (x) = 5 π$

Step 1

Divide each term in $6 \arccos (x) = 5 π$ by $6$ and simplify.

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Step 1.1

Divide each term in $6 \arccos (x) = 5 π$ by $6$ .

$\frac{6 \arccos (x)}{6} = \frac{5 π}{6}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $6$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{6 \arccos (x)}{6} = \frac{5 π}{6}$

Step 1.2.1.2

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

$\arccos (x) = \frac{5 π}{6}$

Step 2

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

$x = \cos (\frac{5 π}{6})$

Step 3

Simplify the right side.

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Step 3.1

Simplify $\cos (\frac{5 π}{6})$ .

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Step 3.1.1

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the second quadrant.

$x = - \cos (\frac{π}{6})$

Step 3.1.2

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

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = - 0.86602540 \dots$