Trigonometry Examples

$(- \frac{8}{17}, \frac{15}{17})$

Step 1

To find the $\tan (θ)$ between the x-axis and the line between the points $(0, 0)$ and $(- \frac{8}{17}, \frac{15}{17})$ , draw the triangle between the three points $(0, 0)$ , $(- \frac{8}{17}, 0)$ , and $(- \frac{8}{17}, \frac{15}{17})$ .

Opposite : $\frac{15}{17}$

Adjacent : $- \frac{8}{17}$

Step 2

$\tan (θ) = \frac{Opposite}{Adjacent}$ therefore $\tan (θ) = \frac{\frac{15}{17}}{- \frac{8}{17}}$ .

$\frac{\frac{15}{17}}{- \frac{8}{17}}$

Step 3

Simplify $\tan (θ)$ .

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Step 3.1

Multiply the numerator by the reciprocal of the denominator.

$\tan (θ) = \frac{15}{17} \cdot (- \frac{17}{8})$

Step 3.2

Cancel the common factor of $17$ .

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Step 3.2.1

Move the leading negative in $- \frac{17}{8}$ into the numerator.

$\tan (θ) = \frac{15}{17} \cdot \frac{- 17}{8}$

Step 3.2.2

Factor $17$ out of $- 17$ .

$\tan (θ) = \frac{15}{17} \cdot \frac{17 (- 1)}{8}$

Step 3.2.3

Cancel the common factor.

$\tan (θ) = \frac{15}{17} \cdot \frac{17 \cdot - 1}{8}$

Step 3.2.4

Rewrite the expression.

$\tan (θ) = 15 (\frac{- 1}{8})$

Step 3.3

Combine $15$ and $\frac{- 1}{8}$ .

$\tan (θ) = \frac{15 \cdot - 1}{8}$

Step 3.4

Simplify the expression.

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Step 3.4.1

Multiply $15$ by $- 1$ .

$\tan (θ) = \frac{- 15}{8}$

Step 3.4.2

Move the negative in front of the fraction.

$\tan (θ) = - \frac{15}{8}$

Step 4

Approximate the result.

$\tan (θ) = - \frac{15}{8} \approx - 1.875$