Question

question
if θ is an angle in standard position and its terminal side passes through the point (-1, -9), find the exact value of tan θ in simplest radical form.
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attempt 1 out of 2
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Explanation:

Step1: Recall the definition of tangent in standard position

For an angle \(\theta\) in standard position with terminal side passing through the point \((x, y)\), the tangent of the angle is given by \(\tan\theta=\frac{y}{x}\) (where \(x
eq0\)).

Step2: Identify \(x\) and \(y\) from the given point

The given point is \((-1, -9)\), so \(x = - 1\) and \(y=-9\).

Step3: Calculate \(\tan\theta\)

Using the formula \(\tan\theta=\frac{y}{x}\), substitute \(x = - 1\) and \(y = - 9\) into it: \(\tan\theta=\frac{-9}{-1}=9\).

Answer:

\(9\)