Double Angle Identities | Explained Visually | with Unit Circle

Understand where the double-angle formulas come from through a visual proof using a right triangle and the unit circle. Follow the triangle’s horizontal and vertical components to build the sine and cosine formulas. Watch the algebra transform between the three cosine forms, then derive the tangent formula step by step - including when it is undefined. Includes: Clear explanations of the angles and component directions. Animated substitutions and colour-coded symbols. An exact-value example using sin θ = 3/5. A practice question with thinking time and a quadrant check. Pause at the practice question and try it before watching the solution. Chapters 0:00 Double the angle, not the value 0:38 Rotate the unit-circle triangle 1:27 Resolve the first step 1:41 Why the second-step angle is θ 2:23 Build the sine and cosine formulas 3:11 Animate the three cosine forms 3:54 Derive tan(2θ) step by step 5:30 Worked example: sin θ = 3/5 6:31 Your turn: θ = 60° 6:55 Solution and quadrant check 7:59 Summary of steps If you found this video useful, like this video and subscribe for more visual maths lessons. #Trigonometry #DoubleAngle #Maths