Trigonometry Examples

$(- 3, - \frac{7 π}{6})$

Step 1

To find the $\tan (θ)$ between the x-axis and the line between the points $(0, 0)$ and $(- 3, - \frac{7 π}{6})$ , draw the triangle between the three points $(0, 0)$ , $(- 3, 0)$ , and $(- 3, - \frac{7 π}{6})$ .

Opposite : $- \frac{7 π}{6}$

Adjacent : $- 3$

Step 2

$\tan (θ) = \frac{Opposite}{Adjacent}$ therefore $\tan (θ) = \frac{- \frac{7 π}{6}}{- 3}$ .

$\frac{- \frac{7 π}{6}}{- 3}$

Step 3

Simplify $\tan (θ)$ .

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Step 3.1

Multiply the numerator by the reciprocal of the denominator.

$\tan (θ) = - \frac{7 π}{6} \cdot \frac{1}{- 3}$

Step 3.2

Move the negative in front of the fraction.

$\tan (θ) = - \frac{7 π}{6} \cdot (- \frac{1}{3})$

Step 3.3

Multiply $- \frac{7 π}{6} (- \frac{1}{3})$ .

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Step 3.3.1

Multiply $- 1$ by $- 1$ .

$\tan (θ) = 1 (\frac{7 π}{6}) \cdot \frac{1}{3}$

Step 3.3.2

Multiply $\frac{7 π}{6}$ by $1$ .

$\tan (θ) = \frac{7 π}{6} \cdot \frac{1}{3}$

Step 3.3.3

Multiply $\frac{7 π}{6}$ by $\frac{1}{3}$ .

$\tan (θ) = \frac{7 π}{6 \cdot 3}$

Step 3.3.4

Multiply $6$ by $3$ .

$\tan (θ) = \frac{7 π}{18}$

Step 4

Approximate the result.

$\tan (θ) = \frac{7 π}{18} \approx 1.22173047$