Question

if $\theta$ is an angle in standard position and its terminal side passes through the point $(1, -4)$, find the exact value of $\tan \theta$ in simplest radical form.

Explanation:

Step1: Recall the definition of tangent

For an angle \(\theta\) in standard position with terminal side passing through \((x,y)\), \(\tan\theta=\frac{y}{x}\).
Here, \(x = 1\) and \(y=- 4\).

Step2: Calculate \(\tan\theta\)

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

Answer:

\(-4\)