A proof to remember: Double Angle Formulas I (visual proof)

This is a short, animated visual proof of the Double angle identities for sine and cosine. To get the formulas we employ the Law of Sines and the Law of Cosines to an isosceles triangle created by from a reflected copy of a given triangle.
If you like this video, consider subscribing to the channel or consider buying me a coffee: www.buymeacoffee.com/VisualPr.... Thanks!
This animation is the classic visual proof the fact but most likely not the one Euclid used.
For visual proofs of the Law of Sines and Law of Cosines, check out:
• Law of Sines Visual Proof
• Law Of Cosines II (vis... or
• Law Of Cosines I (visu...
This animation is based on a visual proof by Sidney H. Kung from the March 1996 issue of The College Mathematics Journal (www.jstor.org/stable/2687407 - page 155).
#mathshorts #mathvideo #math #trigonometry #lawofsines #lawofcosines #triangle #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #circle #obtuseangle #acuteangle #angle #trigidentities #identity #righttriangle #isoscelestriangle #doubleangle
To learn more about animating with manim, check out:
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[@MemeII481]

Omg, I need this! When I learn Maths, I’d rather understanding things than remembering things. However, most teachers just told me to remember it cuz it’s easier. You help me especially with the animation, you made it look so simple. Thanks!

[@MathVisualProofs]

Glad it helped!

[@TheBeardedMathMan]

Superb visual proof! Thank you.

[@MathVisualProofs]

Thank you too!

[@ciaucia156]

initially, area of green triangle
= 2 * 1/2 * sinX * cosX
in terms of base and height
= 1/2 * 1 * sin2X
...

[@alicenthia_GL]

Thank You! Great explanation!

[@MathVisualProofs]

Glad it was helpful!

[@SolLederman]

Love this!

[@MathVisualProofs]

👍😀

[@mtwoh]

Useful. Thank you.

[@MathVisualProofs]

Glad it was helpful!

[@ninnn3025]

great proof, thanks

[@MathVisualProofs]

Glad you like it!

[@ARABICAFRIDAHSONG105]

Angle mathematically visual proof. ✨

[@MathVisualProofs]

:)

[@user-xj7hz7on7v]

nice!

[@MathVisualProofs]

Thanks for checking it out!

[@user-ee4lc6bf1k]

Thank you so much, it's awesome! I need a video about tangent and cotangent too🥴

[@MathVisualProofs]

👍

[@patricialim6816]

Thank you for making this! In a right angled triangle, we define sinx as opposite over hypotenuse. In this non-right triangle, what is sin2A defined as? Is it the same definition?

[@greedskith6612]

Pww of sum to product trig identity, did you make one of it?

[@MathVisualProofs]

I have one in the works…

[@raulsantinolopezrodriguez8349]

Gracias. Con los gráficos es más entendible ( con masa para comprender).

[@MathVisualProofs]

😀👍

[@roychuang0702]

314 likes .......
This Video is So Pi !!

[@MathVisualProofs]

👍😀

[@Jonagold92]

How can you consider sin from 2 times of the angle when the right angle is not guaranteed?

[@MathVisualProofs]

I am using the law of sines. This doesn’t need a right angle; it works in any triangle. I have a visual proof on the channel about law of sines if you aren’t familiar with it.

[@Jonagold92]

@@MathVisualProofs Thanks!

[@anyoung1818]

First!