Questions: What is tan β?

Transcript text: New Definitions - Part II What is $\tan \beta$ ?

Solution

Solution Steps

Step 1: Identify the coordinates

The coordinates given are $(-2, -\sqrt{10})$.

Step 2: Understand the tangent function

The tangent of an angle $\beta$ in a right triangle is defined as the ratio of the opposite side to the adjacent side. In this context, $\tan \beta = \frac{y}{x}$.

Step 3: Apply the coordinates to the tangent function

Using the coordinates $(-2, -\sqrt{10})$: \[ \tan \beta = \frac{-\sqrt{10}}{-2} = \frac{\sqrt{10}}{2} \]

Final Answer

\[ \tan \beta = \frac{\sqrt{10}}{2} \]

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