Trigonometry Examples

$4 \arccos (x) - 2 π = 2 \arccos (x)$

Step 1

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

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Step 1.1

Subtract $2 \arccos (x)$ from both sides of the equation.

$4 \arccos (x) - 2 π - 2 \arccos (x) = 0$

Step 1.2

Subtract $2 \arccos (x)$ from $4 \arccos (x)$ .

$2 \arccos (x) - 2 π = 0$

Step 2

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

$2 \arccos (x) = 2 π$

Step 3

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

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Step 3.1

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

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

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $2$ .

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Step 3.2.1.1

Cancel the common factor.

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

Step 3.2.1.2

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

$\arccos (x) = \frac{2 π}{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Cancel the common factor of $2$ .

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Step 3.3.1.1

Cancel the common factor.

$\arccos (x) = \frac{2 π}{2}$

Step 3.3.1.2

Divide $π$ by $1$ .

$\arccos (x) = π$

Step 4

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

$x = \cos (π)$

Step 5

Simplify the right side.

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Step 5.1

Simplify $\cos (π)$ .

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Step 5.1.1

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.

$x = - \cos (0)$

Step 5.1.2

The exact value of $\cos (0)$ is $1$ .

$x = - 1 \cdot 1$

Step 5.1.3

Multiply $- 1$ by $1$ .

$x = - 1$