Trigonometry Examples

$(\frac{7}{25}, - \frac{24}{25})$

Step 1

To find the $\tan (θ)$ between the x-axis and the line between the points $(0, 0)$ and $(\frac{7}{25}, - \frac{24}{25})$ , draw the triangle between the three points $(0, 0)$ , $(\frac{7}{25}, 0)$ , and $(\frac{7}{25}, - \frac{24}{25})$ .

Opposite : $- \frac{24}{25}$

Adjacent : $\frac{7}{25}$

Step 2

$\tan (θ) = \frac{Opposite}{Adjacent}$ therefore $\tan (θ) = \frac{- \frac{24}{25}}{\frac{7}{25}}$ .

$\frac{- \frac{24}{25}}{\frac{7}{25}}$

Step 3

Simplify $\tan (θ)$ .

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Step 3.1

Multiply the numerator by the reciprocal of the denominator.

$\tan (θ) = - \frac{24}{25} \cdot \frac{25}{7}$

Step 3.2

Cancel the common factor of $25$ .

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Step 3.2.1

Move the leading negative in $- \frac{24}{25}$ into the numerator.

$\tan (θ) = \frac{- 24}{25} \cdot \frac{25}{7}$

Step 3.2.2

Cancel the common factor.

$\tan (θ) = \frac{- 24}{25} \cdot \frac{25}{7}$

Step 3.2.3

Rewrite the expression.

$\tan (θ) = - 24 (\frac{1}{7})$

Step 3.3

Combine $- 24$ and $\frac{1}{7}$ .

$\tan (θ) = \frac{- 24}{7}$

Step 3.4

Move the negative in front of the fraction.

$\tan (θ) = - \frac{24}{7}$

Step 4

Approximate the result.

$\tan (θ) = - \frac{24}{7} \approx - 3.\overline{428571}$