Trigonometry Examples

$2 x = \frac{7 π}{6} + 2 k π$

Step 1

Rewrite the equation as $\frac{7 π}{6} + 2 k π = 2 x$ .

$\frac{7 π}{6} + 2 k π = 2 x$

Step 2

Subtract $\frac{7 π}{6}$ from both sides of the equation.

$2 k π = 2 x - \frac{7 π}{6}$

Step 3

Divide each term in $2 k π = 2 x - \frac{7 π}{6}$ by $2 π$ and simplify.

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Step 3.1

Divide each term in $2 k π = 2 x - \frac{7 π}{6}$ by $2 π$ .

$\frac{2 k π}{2 π} = \frac{2 x}{2 π} + \frac{- \frac{7 π}{6}}{2 π}$

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.

$\frac{2 k π}{2 π} = \frac{2 x}{2 π} + \frac{- \frac{7 π}{6}}{2 π}$

Step 3.2.1.2

Rewrite the expression.

$\frac{k π}{π} = \frac{2 x}{2 π} + \frac{- \frac{7 π}{6}}{2 π}$

Step 3.2.2

Cancel the common factor of $π$ .

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Step 3.2.2.1

Cancel the common factor.

$\frac{k π}{π} = \frac{2 x}{2 π} + \frac{- \frac{7 π}{6}}{2 π}$

Step 3.2.2.2

Divide $k$ by $1$ .

$k = \frac{2 x}{2 π} + \frac{- \frac{7 π}{6}}{2 π}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify each term.

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Step 3.3.1.1

Cancel the common factor of $2$ .

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Step 3.3.1.1.1

Cancel the common factor.

$k = \frac{2 x}{2 π} + \frac{- \frac{7 π}{6}}{2 π}$

Step 3.3.1.1.2

Rewrite the expression.

$k = \frac{x}{π} + \frac{- \frac{7 π}{6}}{2 π}$

Step 3.3.1.2

Multiply the numerator by the reciprocal of the denominator.

$k = \frac{x}{π} - \frac{7 π}{6} \cdot \frac{1}{2 π}$

Step 3.3.1.3

Cancel the common factor of $π$ .

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Step 3.3.1.3.1

Move the leading negative in $- \frac{7 π}{6}$ into the numerator.

$k = \frac{x}{π} + \frac{- 7 π}{6} \cdot \frac{1}{2 π}$

Step 3.3.1.3.2

Factor $π$ out of $- 7 π$ .

$k = \frac{x}{π} + \frac{π \cdot - 7}{6} \cdot \frac{1}{2 π}$

Step 3.3.1.3.3

Factor $π$ out of $2 π$ .

$k = \frac{x}{π} + \frac{π \cdot - 7}{6} \cdot \frac{1}{π \cdot 2}$

Step 3.3.1.3.4

Cancel the common factor.

$k = \frac{x}{π} + \frac{π \cdot - 7}{6} \cdot \frac{1}{π \cdot 2}$

Step 3.3.1.3.5

Rewrite the expression.

$k = \frac{x}{π} + \frac{- 7}{6} \cdot \frac{1}{2}$

Step 3.3.1.4

Multiply $\frac{- 7}{6}$ by $\frac{1}{2}$ .

$k = \frac{x}{π} + \frac{- 7}{6 \cdot 2}$

Step 3.3.1.5

Multiply $6$ by $2$ .

$k = \frac{x}{π} + \frac{- 7}{12}$

Step 3.3.1.6

Move the negative in front of the fraction.

$k = \frac{x}{π} - \frac{7}{12}$