Trigonometry Examples

$\frac{2 π}{b} = 3 π$

Step 1

Find the LCD of the terms in the equation.

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Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$b, 1$

The LCM of one and any expression is the expression.

$b$

Step 2

Multiply each term in $\frac{2 π}{b} = 3 π$ by $b$ to eliminate the fractions.

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Multiply each term in $\frac{2 π}{b} = 3 π$ by $b$ .

$\frac{2 π}{b} b = 3 π b$

Simplify the left side.

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Cancel the common factor of $b$ .

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Cancel the common factor.

$\frac{2 π}{b} b = 3 π b$

Rewrite the expression.

$2 π = 3 π b$

Step 3

Solve the equation.

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Rewrite the equation as $3 π b = 2 π$ .

$3 π b = 2 π$

Divide each term in $3 π b = 2 π$ by $3 π$ and simplify.

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Divide each term in $3 π b = 2 π$ by $3 π$ .

$\frac{3 π b}{3 π} = \frac{2 π}{3 π}$

Simplify the left side.

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Cancel the common factor of $3$ .

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Cancel the common factor.

$\frac{3 π b}{3 π} = \frac{2 π}{3 π}$

Rewrite the expression.

$\frac{π b}{π} = \frac{2 π}{3 π}$

Cancel the common factor of $π$ .

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Cancel the common factor.

$\frac{π b}{π} = \frac{2 π}{3 π}$

Divide $b$ by $1$ .

$b = \frac{2 π}{3 π}$

Simplify the right side.

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Cancel the common factor of $π$ .

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Cancel the common factor.

$b = \frac{2 π}{3 π}$

Rewrite the expression.

$b = \frac{2}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$b = \frac{2}{3}$

Decimal Form:

$b = 0.\overline{6}$