Question

the terminal side of an angle in standard position passes through p(-3, -4). what is the value of tanθ?
○ $\tan\theta = -\frac{4}{3}$
○ $\tan\theta = -\frac{3}{4}$
○ $\tan\theta = \frac{3}{4}$
○ $\tan\theta = \frac{4}{3}$

Explanation:

Step1: Recall the definition of tangent in standard position

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

Step2: Identify the values of \(x\) and \(y\) from the point \(P(-3, -4)\)

Here, \(x = - 3\) and \(y=-4\).

Step3: Calculate \(\tan\theta\)

Substitute \(x=-3\) and \(y = - 4\) into the formula \(\tan\theta=\frac{y}{x}\). So, \(\tan\theta=\frac{-4}{-3}=\frac{4}{3}\).

Answer:

\(\tan\theta=\frac{4}{3}\) (the last option: \(\boldsymbol{\tan\theta=\frac{4}{3}}\))