Trigonometry Examples

$f (\frac{π}{6}) = 2 \cos (x) - \cos (2 x)$

Step 1

Simplify the left side.

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Step 1.1

Combine $f$ and $\frac{π}{6}$ .

$\frac{f π}{6} = 2 \cos (x) - \cos (2 x)$

Step 2

Multiply both sides of the equation by $\frac{6}{π}$ .

$\frac{6}{π} \cdot \frac{f π}{6} = \frac{6}{π} (2 \cos (x) - \cos (2 x))$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{6}{π} \cdot \frac{f π}{6}$ .

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Step 3.1.1.1

Cancel the common factor of $6$ .

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Step 3.1.1.1.1

Cancel the common factor.

$\frac{6}{π} \cdot \frac{f π}{6} = \frac{6}{π} (2 \cos (x) - \cos (2 x))$

Step 3.1.1.1.2

Rewrite the expression.

$\frac{1}{π} (f π) = \frac{6}{π} (2 \cos (x) - \cos (2 x))$

Step 3.1.1.2

Cancel the common factor of $π$ .

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Step 3.1.1.2.1

Factor $π$ out of $f π$ .

$\frac{1}{π} (π f) = \frac{6}{π} (2 \cos (x) - \cos (2 x))$

Step 3.1.1.2.2

Cancel the common factor.

$\frac{1}{π} (π f) = \frac{6}{π} (2 \cos (x) - \cos (2 x))$

Step 3.1.1.2.3

Rewrite the expression.

$f = \frac{6}{π} (2 \cos (x) - \cos (2 x))$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{6}{π} (2 \cos (x) - \cos (2 x))$ .

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Step 3.2.1.1

Apply the distributive property.

$f = \frac{6}{π} (2 \cos (x)) + \frac{6}{π} (- \cos (2 x))$

Step 3.2.1.2

Multiply $\frac{6}{π} (2 \cos (x))$ .

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Step 3.2.1.2.1

Combine $2$ and $\frac{6}{π}$ .

$f = \frac{2 \cdot 6}{π} \cos (x) + \frac{6}{π} (- \cos (2 x))$

Step 3.2.1.2.2

Multiply $2$ by $6$ .

$f = \frac{12}{π} \cos (x) + \frac{6}{π} (- \cos (2 x))$

Step 3.2.1.2.3

Combine $\frac{12}{π}$ and $\cos (x)$ .

$f = \frac{12 \cos (x)}{π} + \frac{6}{π} (- \cos (2 x))$

Step 3.2.1.3

Combine $\frac{6}{π}$ and $\cos (2 x)$ .

$f = \frac{12 \cos (x)}{π} - \frac{6 \cos (2 x)}{π}$