Trigonometry Examples

$2 x + \frac{π}{4} = \frac{3 π}{4} + 2 n π$

Step 1

Move all the expressions to the left side of the equation.

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Step 1.1

Subtract $\frac{3 π}{4}$ from both sides of the equation.

$2 x + \frac{π}{4} - \frac{3 π}{4} = 2 n π$

Step 1.2

Subtract $2 n π$ from both sides of the equation.

$2 x + \frac{π}{4} - \frac{3 π}{4} - 2 n π = 0$

Step 2

Simplify $2 x + \frac{π}{4} - \frac{3 π}{4} - 2 n π$ .

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Step 2.1

Combine the numerators over the common denominator.

$2 x - 2 n π + \frac{π - 3 π}{4} = 0$

Step 2.2

Subtract $3 π$ from $π$ .

$2 x - 2 n π + \frac{- 2 π}{4} = 0$

Step 2.3

Simplify each term.

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Step 2.3.1

Cancel the common factor of $- 2$ and $4$ .

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Step 2.3.1.1

Factor $2$ out of $- 2 π$ .

$2 x - 2 n π + \frac{2 (- π)}{4} = 0$

Step 2.3.1.2

Cancel the common factors.

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Step 2.3.1.2.1

Factor $2$ out of $4$ .

$2 x - 2 n π + \frac{2 (- π)}{2 (2)} = 0$

Step 2.3.1.2.2

Cancel the common factor.

$2 x - 2 n π + \frac{2 (- π)}{2 \cdot 2} = 0$

Step 2.3.1.2.3

Rewrite the expression.

$2 x - 2 n π + \frac{- π}{2} = 0$

Step 2.3.2

Move the negative in front of the fraction.

$2 x - 2 n π - \frac{π}{2} = 0$

Step 3

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.