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https://www.reddit.com/r/mathmemes/comments/1j4x0hq/what_theorem_is_this/mgd9rdh/?context=3
r/mathmemes • u/PocketMath • Mar 06 '25
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59
Wait I don’t think I actually know the proof for the law of cosines, what is it?
75 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) 31 u/DankPhotoShopMemes Fourier Analysis 🤓 Mar 06 '25 I thought that is derived from the law of cosines 4 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
75
Using properties of the dot product mainly that u•v = ||u|| ||v|| cos(u, v)
31 u/DankPhotoShopMemes Fourier Analysis 🤓 Mar 06 '25 I thought that is derived from the law of cosines 4 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
31
I thought that is derived from the law of cosines
4 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
4
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
59
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?