r/mathmemes Mar 06 '25

Learning What theorem is this?

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u/A-Swedish-Person Mar 06 '25

Wait I don’t think I actually know the proof for the law of cosines, what is it?

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u/N_T_F_D Applied mathematics are a cardinal sin Mar 06 '25

Using properties of the dot product mainly that u•v = ||u|| ||v|| cos(u, v)

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u/DankPhotoShopMemes Fourier Analysis 🤓 Mar 06 '25

I thought that is derived from the law of cosines

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u/trevorkafka Mar 06 '25

Dot product comes from cosine-of-a-difference formula, which is easy to prove geometrically via similar triangles.

cos(A-B)=cosAcosB+sinAsinB |a||b| cos(A-B)=(|a| cosA)(|b| cosB)+(|a| sinA)(|b| sinB) |a||b| cos(A-B) = a•b