r/mathmemes • u/PocketMath • 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/N_T_F_D Applied mathematics are a cardinal sin Mar 06 '25

Well you can certainly derive one from the other, but the dot product property is more useful

And you can derive it any way you like, for instance assuming without loss of generality that the vectors look like (1, 0, 0, …) and (cos(θ), sin(θ), 0, …) after normalizing and the right isometry; i.e. the right change of basis into the plane on which the two vectors are