The law of cosines is Pythagoras with a correction
A triangle with sides a and b and included angle C morphs while c is computed live from c squared equals a squared plus b squared minus 2ab cos C. Watching the correction term shrink to zero at 90 degrees, grow for obtuse angles, and reverse sign for acute angles builds intuition for how the Law of Cosines generalizes the Pythagorean theorem. Useful for trigonometry students learning triangle solving and for teachers introducing non-right triangles.
16:9 · Preview before teaching · automatic layout checks do not establish subject accuracy
The prompt that made it
Apply ALL of the following review notes precisely; keep everything else identical. This video is for social media and must be impeccable. - Mmmm the flow of this video is a bit off, we need better timings, not so much information given so quickly
Make the next one in this series
- Show the Law of Sines with the same triangle and live ratio values as angles change.
- Animate deriving the Law of Cosines from dropping a perpendicular height in the triangle.
- Compare Law of Cosines versus Pythagorean theorem side by side as angle C sweeps to 90 degrees.
