Precalculus Examples

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

Step 1

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

Step 2

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

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

Step 3

Simplify $\tan (θ)$ .

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Step 3.1

Dividing two negative values results in a positive value.

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

Step 3.2

Multiply the numerator by the reciprocal of the denominator.

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

Step 3.3

Cancel the common factor of $61$ .

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Step 3.3.1

Cancel the common factor.

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

Step 3.3.2

Rewrite the expression.

$\tan (θ) = 11 (\frac{1}{60})$

Step 3.4

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

$\tan (θ) = \frac{11}{60}$

Step 4

Approximate the result.

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