Trigonometry Examples

$\cos (\frac{1}{9} x) = \cos (\frac{1}{2} x)$

Step 1

For the two functions to be equal, the arguments of each must be equal.

$\frac{1}{9} x = \frac{1}{2} x$

Step 2

Simplify both sides.

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Step 2.1

Combine $\frac{1}{9}$ and $x$ .

$\frac{x}{9} = \frac{1}{2} x$

Step 2.2

Combine $\frac{1}{2}$ and $x$ .

$\frac{x}{9} = \frac{x}{2}$

Step 3

Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.

$x \cdot 2 = 9 x$

Step 4

Solve the equation for $x$ .

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Step 4.1

Move $2$ to the left of $x$ .

$2 x = 9 x$

Step 4.2

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

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Step 4.2.1

Subtract $9 x$ from both sides of the equation.

$2 x - 9 x = 0$

Step 4.2.2

Subtract $9 x$ from $2 x$ .

$- 7 x = 0$

Step 4.3

Divide each term in $- 7 x = 0$ by $- 7$ and simplify.

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Step 4.3.1

Divide each term in $- 7 x = 0$ by $- 7$ .

$\frac{- 7 x}{- 7} = \frac{0}{- 7}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $- 7$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{- 7 x}{- 7} = \frac{0}{- 7}$

Step 4.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{0}{- 7}$

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Divide $0$ by $- 7$ .

$x = 0$