Trigonometry · Intermediate · 9 min
Angle addition
Angle addition is vector addition in a rotated coordinate frame.
WHAT HAPPENS IF…Why does the cosine formula contain a subtraction?
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In the rotated frame, the unit vector has components cosβ and sinβ. Its basis vectors are (cosα,sinα) and (−sinα,cosα). Multiplying and adding gives both the cosine formula and sin(α+β)=sinα cosβ+cosα sinβ.
A detail that matters
In general cos(α+β) is not cosα+cosβ.
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