Questions: Find tan α.

Transcript text: Find $\tan \alpha$.

Solution

Solution Steps

Step 1: Identify the coordinates

The coordinates given are $(\sqrt{5}, -\sqrt{7})$.

Step 2: Recall the formula for tangent

The tangent of an angle $\alpha$ in a right triangle is given by the ratio of the opposite side to the adjacent side. In this case, $\tan \alpha = \frac{y}{x}$.

Step 3: Substitute the coordinates into the formula

Here, $x = \sqrt{5}$ and $y = -\sqrt{7}$. So, $\tan \alpha = \frac{-\sqrt{7}}{\sqrt{5}}$.

Final Answer

\[ \tan \alpha = -\sqrt{\frac{7}{5}} \]

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