Find the Tangent Given the Point (-35/37,-12/37)

$(- \frac{35}{37}, - \frac{12}{37})$

Step 1

To find the $\tan (θ)$ between the x-axis and the line between the points $(0, 0)$ and $(- \frac{35}{37}, - \frac{12}{37})$ , draw the triangle between the three points $(0, 0)$ , $(- \frac{35}{37}, 0)$ , and $(- \frac{35}{37}, - \frac{12}{37})$ .

Opposite : $- \frac{12}{37}$

Adjacent : $- \frac{35}{37}$

Step 2

$\tan (θ) = \frac{Opposite}{Adjacent}$ therefore $\tan (θ) = \frac{- \frac{12}{37}}{- \frac{35}{37}}$ .

$\frac{- \frac{12}{37}}{- \frac{35}{37}}$

Step 3

Simplify $\tan (θ)$ .

Dividing two negative values results in a positive value.

$\tan (θ) = \frac{\frac{12}{37}}{\frac{35}{37}}$

Multiply the numerator by the reciprocal of the denominator.

$\tan (θ) = \frac{12}{37} \cdot \frac{37}{35}$

Cancel the common factor of $37$ .

Cancel the common factor.

$\tan (θ) = \frac{12}{37} \cdot \frac{37}{35}$

Rewrite the expression.

$\tan (θ) = 12 (\frac{1}{35})$

Combine $12$ and $\frac{1}{35}$ .

$\tan (θ) = \frac{12}{35}$

Step 4

Approximate the result.

$\tan (θ) = \frac{12}{35} \approx 0.3\overline{428571}$

Find the Tangent Given the Point (-35/37,-12/37)

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