Trigonometry Examples

$f (\frac{π}{3}) = 2 \sin (x) + \cos (3 x)$

Step 1

Simplify the left side.

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Step 1.1

Combine $f$ and $\frac{π}{3}$ .

$\frac{f π}{3} = 2 \sin (x) + \cos (3 x)$

Step 2

Multiply both sides of the equation by $\frac{3}{π}$ .

$\frac{3}{π} \cdot \frac{f π}{3} = \frac{3}{π} (2 \sin (x) + \cos (3 x))$

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 $\frac{3}{π} \cdot \frac{f π}{3}$ .

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Step 3.1.1.1

Cancel the common factor of $3$ .

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Step 3.1.1.1.1

Cancel the common factor.

$\frac{3}{π} \cdot \frac{f π}{3} = \frac{3}{π} (2 \sin (x) + \cos (3 x))$

Step 3.1.1.1.2

Rewrite the expression.

$\frac{1}{π} (f π) = \frac{3}{π} (2 \sin (x) + \cos (3 x))$

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 $f π$ .

$\frac{1}{π} (π f) = \frac{3}{π} (2 \sin (x) + \cos (3 x))$

Step 3.1.1.2.2

Cancel the common factor.

$\frac{1}{π} (π f) = \frac{3}{π} (2 \sin (x) + \cos (3 x))$

Step 3.1.1.2.3

Rewrite the expression.

$f = \frac{3}{π} (2 \sin (x) + \cos (3 x))$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{3}{π} (2 \sin (x) + \cos (3 x))$ .

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Step 3.2.1.1

Apply the distributive property.

$f = \frac{3}{π} (2 \sin (x)) + \frac{3}{π} \cos (3 x)$

Step 3.2.1.2

Multiply $\frac{3}{π} (2 \sin (x))$ .

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Step 3.2.1.2.1

Combine $2$ and $\frac{3}{π}$ .

$f = \frac{2 \cdot 3}{π} \sin (x) + \frac{3}{π} \cos (3 x)$

Step 3.2.1.2.2

Multiply $2$ by $3$ .

$f = \frac{6}{π} \sin (x) + \frac{3}{π} \cos (3 x)$

Step 3.2.1.2.3

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

$f = \frac{6 \sin (x)}{π} + \frac{3}{π} \cos (3 x)$

Step 3.2.1.3

Combine $\frac{3}{π}$ and $\cos (3 x)$ .

$f = \frac{6 \sin (x)}{π} + \frac{3 \cos (3 x)}{π}$