Questions: Find the value of tan θ if the point P lies on the terminal side of θ. P(3,-4) a. -4/3 b. 4/3 c. -3/4 d. 3/4

Solution Steps

To find the value of \(\tan \theta\) given a point \(P(x, y)\) on the terminal side of \(\theta\), we use the definition of the tangent function in terms of the coordinates of the point. Specifically, \(\tan \theta = \frac{y}{x}\).

Given the point \(P(3, -4)\):

• \(x = 3\)
• \(y = -4\)

We can now calculate \(\tan \theta\).

Given the point \( P(3, -4) \), we have:

• \( x = 3 \)
• \( y = -4 \)

Using the definition of the tangent function: \[ \tan \theta = \frac{y}{x} = \frac{-4}{3} \]

The value of \( \tan \theta \) is: \[ \tan \theta = -\frac{4}{3} \]

Final Answer