Trigonometry Examples

$y = - 2 + (\frac{1}{2}) \cdot \tan (\frac{0}{2} + \frac{5 π}{6})$

Step 1

Rewrite in slope-intercept form.

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Step 1.1

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Step 1.2

Write in $y = m x + b$ form.

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Step 1.2.1

To write $- 2$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$y = - 2 \cdot \frac{6}{6} - \frac{\sqrt{3}}{6}$

Step 1.2.2

Combine $- 2$ and $\frac{6}{6}$ .

$y = \frac{- 2 \cdot 6}{6} - \frac{\sqrt{3}}{6}$

Step 1.2.3

Combine the numerators over the common denominator.

$y = \frac{- 2 \cdot 6 - \sqrt{3}}{6}$

Step 1.2.4

Multiply $- 2$ by $6$ .

$y = \frac{- 12 - \sqrt{3}}{6}$

Step 1.2.5

Rewrite $- 12$ as $- 1 (12)$ .

$y = \frac{- 1 (12) - \sqrt{3}}{6}$

Step 1.2.6

Factor $- 1$ out of $- \sqrt{3}$ .

$y = \frac{- 1 (12) - (\sqrt{3})}{6}$

Step 1.2.7

Factor $- 1$ out of $- 1 (12) - (\sqrt{3})$ .

$y = \frac{- 1 (12 + \sqrt{3})}{6}$

Step 1.2.8

Move the negative in front of the fraction.

$y = - \frac{12 + \sqrt{3}}{6}$

Step 2

Use the slope-intercept form to find the slope and y-intercept.

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Step 2.1

Find the values of $m$ and $b$ using the form $y = m x + b$ .

$m = 0$

$b = - \frac{12 + \sqrt{3}}{6}$

Step 2.2

The slope of the line is the value of $m$ , and the y-intercept is the value of $b$ .

Slope: $0$

y-intercept: $(0, - \frac{12 + \sqrt{3}}{6})$

Slope: $0$

y-intercept: $(0, - \frac{12 + \sqrt{3}}{6})$

Step 3

Find two points on the line.

$\begin{array}{c} x & y \\ 0 & - 2 - \frac{\sqrt{3}}{6} \\ 1 & - 2 - \frac{\sqrt{3}}{6} \end{array}$

Step 4

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

Slope: $0$

y-intercept: $(0, - \frac{12 + \sqrt{3}}{6})$

$\begin{array}{c} x & y \\ 0 & - 2 - \frac{\sqrt{3}}{6} \\ 1 & - 2 - \frac{\sqrt{3}}{6} \end{array}$

Step 5