[eli5] why is gradient = tangent theta?

Question

[eli5] why is gradient = tangent theta?

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Answer 1

tan(θ) is defined as sin(θ)/cos(θ). Which could also be rewritten as “rise”/”run”, since sin(θ) represents the vertical component of the angle, and cos(θ) represents the horizontal component. And rise/run is the description of a slope or gradient.