Trigonometry Examples

$x - \frac{π}{6} = \frac{π}{2}$

Step 1

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

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Step 1.1

Add $\frac{π}{6}$ to both sides of the equation.

$x = \frac{π}{2} + \frac{π}{6}$

Step 1.2

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

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

Step 1.3

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

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Step 1.3.1

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

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

Step 1.3.2

Multiply $2$ by $3$ .

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

Step 1.4

Combine the numerators over the common denominator.

$x = \frac{π \cdot 3 + π}{6}$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Move $3$ to the left of $π$ .

$x = \frac{3 \cdot π + π}{6}$

Step 1.5.2

Add $3 π$ and $π$ .

$x = \frac{4 π}{6}$

Step 1.6

Cancel the common factor of $4$ and $6$ .

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Step 1.6.1

Factor $2$ out of $4 π$ .

$x = \frac{2 (2 π)}{6}$

Step 1.6.2

Cancel the common factors.

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Step 1.6.2.1

Factor $2$ out of $6$ .

$x = \frac{2 (2 π)}{2 (3)}$

Step 1.6.2.2

Cancel the common factor.

$x = \frac{2 (2 π)}{2 \cdot 3}$

Step 1.6.2.3

Rewrite the expression.

$x = \frac{2 π}{3}$

Step 2

Since $x = \frac{2 π}{3}$ is a vertical line, there is no y-intercept and the slope is undefined.

Slope: Undefined

y-intercept: No y-intercept

Step 3

Find two points on the line.

$\begin{array}{c} x & y \\ \frac{2 π}{3} & 0 \\ \frac{2 π}{3} & 1 \end{array}$

Step 4

Graph the line using the slope, y-intercept, and two points.

Slope: Undefined

y-intercept: No y-intercept

$\begin{array}{c} x & y \\ \frac{2 π}{3} & 0 \\ \frac{2 π}{3} & 1 \end{array}$

Step 5