The point P(3, 4) is on the terminal side of θ. Evaluate tan θ.

Solution:

Given,

The point P(3,4) is on the terminal side of θ.

tanθ = perpendicular/base

tanθ = 4/3

Or

The slope can be found using the formula

m = tanθ = y₂ - y₁/ x₂ - x₁

From the figure we know that the two points are

(0, 0) and (3, 4)

Substituting the values in the given formula

tanθ = 4 - 0/3 -0

So we get

tanθ = 4/3

Therefore, tanθ = 4/3

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The point P(3, 4) is on the terminal side of θ. Evaluate tan θ.

Summary:

The point P(3, 4) is on the terminal side of θ. tan θ = 4/3.