Precalculus Examples

$(10, - 8)$

Step 1

To find the $\tan (θ)$ between the x-axis and the line between the points $(0, 0)$ and $(10, - 8)$ , draw the triangle between the three points $(0, 0)$ , $(10, 0)$ , and $(10, - 8)$ .

Opposite : $- 8$

Adjacent : $10$

Step 2

$\tan (θ) = \frac{Opposite}{Adjacent}$ therefore $\tan (θ) = \frac{- 8}{10}$ .

$\frac{- 8}{10}$

Step 3

Simplify $\tan (θ)$ .

Tap for more steps...

Step 3.1

Cancel the common factor of $- 8$ and $10$ .

Tap for more steps...

Step 3.1.1

Factor $2$ out of $- 8$ .

$\tan (θ) = \frac{2 (- 4)}{10}$

Step 3.1.2

Cancel the common factors.

Tap for more steps...

Step 3.1.2.1

Factor $2$ out of $10$ .

$\tan (θ) = \frac{2 \cdot - 4}{2 \cdot 5}$

Step 3.1.2.2

Cancel the common factor.

$\tan (θ) = \frac{2 \cdot - 4}{2 \cdot 5}$

Step 3.1.2.3

Rewrite the expression.

$\tan (θ) = \frac{- 4}{5}$

Step 3.2

Move the negative in front of the fraction.

$\tan (θ) = - \frac{4}{5}$

Step 4

Approximate the result.

$\tan (θ) = - \frac{4}{5} \approx - 0.8$