Trigonometry Examples

$\arccos (5 x) = π$

Step 1

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

$5 x = \cos (π)$

Step 2

Simplify the right side.

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Step 2.1

Simplify $\cos (π)$ .

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Step 2.1.1

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.

$5 x = - \cos (0)$

Step 2.1.2

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

$5 x = - 1 \cdot 1$

Step 2.1.3

Multiply $- 1$ by $1$ .

$5 x = - 1$

Step 3

Divide each term in $5 x = - 1$ by $5$ and simplify.

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Step 3.1

Divide each term in $5 x = - 1$ by $5$ .

$\frac{5 x}{5} = \frac{- 1}{5}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $5$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{5 x}{5} = \frac{- 1}{5}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 1}{5}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Move the negative in front of the fraction.

$x = - \frac{1}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{1}{5}$

Decimal Form:

$x = - 0.2$