Trigonometry Examples

$2 x - \frac{π}{3} = \frac{3 π}{2}$

Step 1

Move all terms not containing $x$ to the right side of the equation.

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Step 1.1

Add $\frac{π}{3}$ to both sides of the equation.

$2 x = \frac{3 π}{2} + \frac{π}{3}$

Step 1.2

To write $\frac{3 π}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$2 x = \frac{3 π}{2} \cdot \frac{3}{3} + \frac{π}{3}$

Step 1.3

To write $\frac{π}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$2 x = \frac{3 π}{2} \cdot \frac{3}{3} + \frac{π}{3} \cdot \frac{2}{2}$

Step 1.4

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.4.1

Multiply $\frac{3 π}{2}$ by $\frac{3}{3}$ .

$2 x = \frac{3 π \cdot 3}{2 \cdot 3} + \frac{π}{3} \cdot \frac{2}{2}$

Step 1.4.2

Multiply $2$ by $3$ .

$2 x = \frac{3 π \cdot 3}{6} + \frac{π}{3} \cdot \frac{2}{2}$

Step 1.4.3

Multiply $\frac{π}{3}$ by $\frac{2}{2}$ .

$2 x = \frac{3 π \cdot 3}{6} + \frac{π \cdot 2}{3 \cdot 2}$

Step 1.4.4

Multiply $3$ by $2$ .

$2 x = \frac{3 π \cdot 3}{6} + \frac{π \cdot 2}{6}$

Step 1.5

Combine the numerators over the common denominator.

$2 x = \frac{3 π \cdot 3 + π \cdot 2}{6}$

Step 1.6

Simplify the numerator.

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Step 1.6.1

Multiply $3$ by $3$ .

$2 x = \frac{9 π + π \cdot 2}{6}$

Step 1.6.2

Move $2$ to the left of $π$ .

$2 x = \frac{9 π + 2 \cdot π}{6}$

Step 1.6.3

Add $9 π$ and $2 π$ .

$2 x = \frac{11 π}{6}$

Step 2

Divide each term in $2 x = \frac{11 π}{6}$ by $2$ and simplify.

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Step 2.1

Divide each term in $2 x = \frac{11 π}{6}$ by $2$ .

$\frac{2 x}{2} = \frac{\frac{11 π}{6}}{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $2$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{\frac{11 π}{6}}{2}$

Step 2.2.1.2

Divide $x$ by $1$ .

$x = \frac{\frac{11 π}{6}}{2}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Multiply the numerator by the reciprocal of the denominator.

$x = \frac{11 π}{6} \cdot \frac{1}{2}$

Step 2.3.2

Multiply $\frac{11 π}{6} \cdot \frac{1}{2}$ .

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Step 2.3.2.1

Multiply $\frac{11 π}{6}$ by $\frac{1}{2}$ .

$x = \frac{11 π}{6 \cdot 2}$

Step 2.3.2.2

Multiply $6$ by $2$ .

$x = \frac{11 π}{12}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{11 π}{12}$

Decimal Form:

$x = 2.87979326 \dots$