Question

question if θ is an angle in standard position and its terminal side passes through the point (1, -4), find the exact value of tan θ in simplest radical form. answer attempt 1 out of 2

Explanation:

Step1: Recall the formula for tangent

The formula for \(\tan\theta=\frac{y}{x}\) when the terminal side of the angle \(\theta\) in standard position passes through the point \((x,y)\).

Step2: Identify \(x\) and \(y\) values

Given the point \((1, - 4)\), we have \(x = 1\) and \(y=-4\).

Step3: Calculate \(\tan\theta\)

Substitute \(x = 1\) and \(y =-4\) into the formula \(\tan\theta=\frac{y}{x}\), so \(\tan\theta=\frac{-4}{1}=-4\).

Answer:

\(-4\)