Video yükleniyor...

Video Yüklenemedi

Ana Sayfaya Dön

Why sin²θ + cos²θ =1? A Geometric Proof.

stemexplor's profile picture

S.T.E.M Explorer

57,589 subscribers

36,003 görüntüleme • 7 ay önce •via X (Twitter)

EğitimBilim & Teknoloji
LIVE

Anya Rossi• Live Now

Private livecam show

3 Yorum

Naczelny Matematyk Kraju 📐➕️🪔🟰🤑 profil fotoğrafı
Naczelny Matematyk Kraju 📐➕️🪔🟰🤑7 ay önce

a²+b²=c² (a/c)²+(b/c)²=(c/c)² sin²x+cos²x=1.

Joseph Cusick profil fotoğrafı
Joseph Cusick7 ay önce

The Pythagorean Theorem is the equation of the circle yet has no pi.

tom david profil fotoğrafı
tom david7 ay önce

👍

Benzer Videolar

Finally got to know the real use of Sin θ/Cos θ …!💀🔥🙌🏼
2:44

Finally got to know the real use of Sin θ/Cos θ …!💀🔥🙌🏼

Ravi Tiwari🇮🇳

40,643 görüntüleme • 7 ay önce

The geometry of eⁱᶿ = cos(θ) + isin(θ).
0:20

The geometry of eⁱᶿ = cos(θ) + isin(θ).

The Math Flow

19,986 görüntüleme • 4 ay önce

A point traces each closed mathematical curve at constant speed. Its vertical coordinate versus elapsed time produces a unique periodic waveform. 4-petal rose r = a cos(2θ). Astroid hypocycloid x = a cos³θ, y = a sin³θ. Squircle |x|⁴ + |y|⁴ = a⁴. 4-cusped epicycloid. Heart curve (x² + y² - 1)³ = x² y³.
0:23

A point traces each closed mathematical curve at constant speed. Its vertical coordinate versus elapsed time produces a unique periodic waveform. 4-petal rose r = a cos(2θ). Astroid hypocycloid x = a cos³θ, y = a sin³θ. Squircle |x|⁴ + |y|⁴ = a⁴. 4-cusped epicycloid. Heart curve (x² + y² - 1)³ = x² y³.

Matheorems

10,618 görüntüleme • 1 ay önce

ہمیں پڑھایا کچھ اور جا رہا ہے زندگی میں کام کچھ اور آ رہا ہے relevant پڑھائی نہیں ہے کیا کسی نے a^2+b^2+2ab کا فارمولہ استعمال کر کے بازار سے کیلے خریدے ؟ tan θ cos θ زندگی میں کام آیا ؟ لیکن سب سے زیادہ نیند اسی tan θ cos θ نے حرام کی ! بھگونت مان 🤣
0:34

ہمیں پڑھایا کچھ اور جا رہا ہے زندگی میں کام کچھ اور آ رہا ہے relevant پڑھائی نہیں ہے کیا کسی نے a^2+b^2+2ab کا فارمولہ استعمال کر کے بازار سے کیلے خریدے ؟ tan θ cos θ زندگی میں کام آیا ؟ لیکن سب سے زیادہ نیند اسی tan θ cos θ نے حرام کی ! بھگونت مان 🤣

AMJAD KHAN

28,261 görüntüleme • 2 ay önce

“٩ﾉ( ＾ᗜ＾)θ♬゜ #SDVX
0:33

“٩ﾉ( ＾ᗜ＾)θ♬゜ #SDVX

SOUND VOLTEX STAFF

698,389 görüntüleme • 1 yıl önce

🎶🎸(❛▽❛)✨♪( ´θ｀)🥁🎶!!
0:23

🎶🎸(❛▽❛)✨♪( ´θ｀)🥁🎶!!

✨内田清輝・グ弍✨

114,491 görüntüleme • 2 yıl önce

ブラジル人にウケる一発ギャグ(θヮθ) (ﾉﾉ_☆)ｗｗｗｗｗｗ
0:24

ブラジル人にウケる一発ギャグ(θヮθ) (ﾉﾉ_☆)ｗｗｗｗｗｗ

コ タ ツ ミ

91,724 görüntüleme • 9 ay önce

What Curve Beats a Straight Line? Take two fixed points A and B. A bead slides without friction under gravity. Among all possible curves connecting A to B, which one gives the smallest travel time? This is the Brachistochrone problem. The time functional is T[y] = ∫ √((1 + y′²)/(2gy)) dx where y is the vertical drop from the starting point. The winning curve is not a straight line. It is a cycloid x(θ) = a(θ - sin θ) y(θ) = a(1 - cos θ) The bead first falls steeply to gain speed, then uses that speed across the remaining distance. The path is longer than the straight segment, yet the travel time is smaller. The shortest path solves geometry. The fastest path solves variation. #CalculusOfVariations #Brachistochrone #Cycloid #ClassicalMechanics #MathematicalPhysics #Optimization #DifferentialEquations #PhysicsAnimation #Mathematics
0:55

What Curve Beats a Straight Line? Take two fixed points A and B. A bead slides without friction under gravity. Among all possible curves connecting A to B, which one gives the smallest travel time? This is the Brachistochrone problem. The time functional is T[y] = ∫ √((1 + y′²)/(2gy)) dx where y is the vertical drop from the starting point. The winning curve is not a straight line. It is a cycloid x(θ) = a(θ - sin θ) y(θ) = a(1 - cos θ) The bead first falls steeply to gain speed, then uses that speed across the remaining distance. The path is longer than the straight segment, yet the travel time is smaller. The shortest path solves geometry. The fastest path solves variation. #CalculusOfVariations #Brachistochrone #Cycloid #ClassicalMechanics #MathematicalPhysics #Optimization #DifferentialEquations #PhysicsAnimation #Mathematics

Mathelirium

17,600 görüntüleme • 4 ay önce

This is points P_k at polar coords (radius = k·r, angle = k·θ) as θ spins. Connect sequentially: • small θ → smooth Archimedean spiral • θ = 2π·p/q → perfect n-gons & stars emerge!
0:20

This is points P_k at polar coords (radius = k·r, angle = k·θ) as θ spins. Connect sequentially: • small θ → smooth Archimedean spiral • θ = 2π·p/q → perfect n-gons & stars emerge!

Mathematica

23,410 görüntüleme • 7 ay önce

I took a Jacobi Theta divisor, Θ(z,t) = ∏ⱼ θ₁(z - cⱼ(t) | τ(t)), and let it breathe across a torus, with the small spheres marking its moving zeros... the precise points where Θ(z,t) vanishes.
0:56

I took a Jacobi Theta divisor, Θ(z,t) = ∏ⱼ θ₁(z - cⱼ(t) | τ(t)), and let it breathe across a torus, with the small spheres marking its moving zeros... the precise points where Θ(z,t) vanishes.

Mathelirium

42,997 görüntüleme • 3 ay önce

실바니안 패밀리 ♪( ´θ｀)
0:25

실바니안 패밀리 ♪( ´θ｀)

시겢

12,566 görüntüleme • 5 ay önce

n₁ sin(θ₁) = n₂ sin(θ₂) This elegant equation describes how light bends at the boundary between two media. Here, n₁ and n₂ are the refractive indices, while θ₁ and θ₂ are the angles of incidence and refraction measured from the surface normal. As light rays obey this simple trigonometric relationship, beautiful caustic curves emerge and focal points shift with every change in geometry or material. It is pure geometric optics at its finest: the raw interaction of light and matter, reminding us that the universe is governed by beautiful, predictable symmetries. This is used while designing high-resolution camera lenses (correcting aberrations for sharp focus) and enabling fiber-optic communication through total internal reflection.
1:05

n₁ sin(θ₁) = n₂ sin(θ₂) This elegant equation describes how light bends at the boundary between two media. Here, n₁ and n₂ are the refractive indices, while θ₁ and θ₂ are the angles of incidence and refraction measured from the surface normal. As light rays obey this simple trigonometric relationship, beautiful caustic curves emerge and focal points shift with every change in geometry or material. It is pure geometric optics at its finest: the raw interaction of light and matter, reminding us that the universe is governed by beautiful, predictable symmetries. This is used while designing high-resolution camera lenses (correcting aberrations for sharp focus) and enabling fiber-optic communication through total internal reflection.

Mathematica

32,988 görüntüleme • 6 ay önce

Και τα κινητά θ ανοίξουν.... #paobc
0:30

Και τα κινητά θ ανοίξουν.... #paobc

NoJoB

18,685 görüntüleme • 3 gün önce

Damso Θ. Macarena Version acoustique ☀️
1:01

Damso Θ. Macarena Version acoustique ☀️

DamsoΣ.MOROSE 🔱

37,948 görüntüleme • 3 yıl önce

n₁ sin θ₁ = n₂ sin θ₂ Watch this laser hit the glass-air boundary. At first, it bends out (refraction). Then... boom. Angle exceeds the critical θ_c = arcsin(n₂/n₁) ≈ 42° for glass (n≈1.5), and every photon turns back inside. No leakage. Pure total internal reflection. This is why fiber optics carry the internet across oceans without losing signal. Why diamonds sparkle like crazy. Why light can get trapped in a stream of water.
0:28

n₁ sin θ₁ = n₂ sin θ₂ Watch this laser hit the glass-air boundary. At first, it bends out (refraction). Then... boom. Angle exceeds the critical θ_c = arcsin(n₂/n₁) ≈ 42° for glass (n≈1.5), and every photon turns back inside. No leakage. Pure total internal reflection. This is why fiber optics carry the internet across oceans without losing signal. Why diamonds sparkle like crazy. Why light can get trapped in a stream of water.

Mathematica

48,423 görüntüleme • 6 ay önce

#ジャンボ文鳥 #茜音 ( ･θ･)ﾁｮｯﾁｮｯﾁｮｯﾁｮﾁﾁﾁﾁﾁﾋﾟｭｰｲ♪
0:54

#ジャンボ文鳥 #茜音 ( ･θ･)ﾁｮｯﾁｮｯﾁｮｯﾁｮﾁﾁﾁﾁﾁﾋﾟｭｰｲ♪

saeko

45,767 görüntüleme • 1 yıl önce

夏乗り切るためにエネルギーチャージϵ( 'Θ' )϶
0:48

夏乗り切るためにエネルギーチャージϵ( 'Θ' )϶

安藤京香

14,545 görüntüleme • 3 ay önce

ひとり夢芝居♪( ´θ｀)ノ #高市モームリ
1:25

ひとり夢芝居♪( ´θ｀)ノ #高市モームリ

武田浩典

95,599 görüntüleme • 4 ay önce