Question

The terminal side of an angle in standard position passes through p(–3, –4). what is the value of tangent theta?

Answer 1

4/3

Explanation:

The tangent of any angle (θ) in standard position that has point (x, y) on its terminal ray is ...

tan(θ) = y/x

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For the given point on the terminal side, the tangent is ...

tan(θ) = (-4)/(-3) = 4/3

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Additional comment

There are several ways this can be explained. One of them makes use of the relation between rectangular and polar coordinates:

(x, y) = (r·cos(θ), r·sin(θ))

Then the ratio y/x is ...

y/x = (r·sin(θ))/(r·cos(θ)) = sin(θ)/cos(θ) = tan(θ)