Find the Tangent Given the Point (-60/61,11/61)

$(- \frac{60}{61}, \frac{11}{61})$

To find the $\tan (θ)$ between the x-axis and the line between the points $(0, 0)$ and $(- \frac{60}{61}, \frac{11}{61})$ , draw the triangle between the three points $(0, 0)$ , $(- \frac{60}{61}, 0)$ , and $(- \frac{60}{61}, \frac{11}{61})$ .

Opposite : $\frac{11}{61}$

Adjacent : $- \frac{60}{61}$

$\tan (θ) = \frac{Opposite}{Adjacent}$ therefore $\tan (θ) = \frac{\frac{11}{61}}{- \frac{60}{61}}$ .

$\frac{\frac{11}{61}}{- \frac{60}{61}}$

Simplify $\tan (θ)$ .

Multiply the numerator by the reciprocal of the denominator.

$\tan (θ) = \frac{11}{61} \cdot (- \frac{61}{60})$

Cancel the common factor of $61$ .

Move the leading negative in $- \frac{61}{60}$ into the numerator.

$\tan (θ) = \frac{11}{61} \cdot \frac{- 61}{60}$

Factor $61$ out of $- 61$ .

$\tan (θ) = \frac{11}{61} \cdot \frac{61 (- 1)}{60}$

Cancel the common factor.

$\tan (θ) = \frac{11}{61} \cdot \frac{61 \cdot - 1}{60}$

Rewrite the expression.

$\tan (θ) = 11 (\frac{- 1}{60})$

Combine $11$ and $\frac{- 1}{60}$ .

$\tan (θ) = \frac{11 \cdot - 1}{60}$

Simplify the expression.

Multiply $11$ by $- 1$ .

$\tan (θ) = \frac{- 11}{60}$

Move the negative in front of the fraction.

$\tan (θ) = - \frac{11}{60}$

Approximate the result.

$\tan (θ) = - \frac{11}{60} \approx - 0.18\overline{3}$

Find the Tangent Given the Point (-60/61,11/61)

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