Trigonometry · Intermediate · 9 min
Trigonometry in polar form
Sine and cosine translate a radial description into Cartesian coordinates.
WHAT HAPPENS IF…Can a point have more than one polar description?
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The unit direction at angle θ is (cosθ,sinθ). Multiplying by r scales it, and a negative r reverses it. Thus (r,θ) and (−r,θ+π) describe the same point. At r=0 every angle names the origin.
A detail that matters
The geometric distance is |r| when signed radii are allowed.
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