Why is sin 150° = 0.5? The unit circle explained from a bowstring

Type sin 150° into any calculator: it says 0.5. But no right triangle has a 150° corner. So what is the calculator measuring? The answer is the unit circle, and a 1,500-year-old word for a bowstring. In this video: why 'opposite over hypotenuse' breaks past 90°; Aryabhata's ardha-jya (half a bowstring, 499 CE) and how a misread Arabic word turned it into sinus, a fold; trigonometric functions defined with the unit circle, as the horizontal and vertical projections of a turning arrow; why sin 150° = sin 30° = ½; positive and negative angles; the signs of sin and cos in the four quadrants; why sin x and cos x stay between −1 and 1; why sin²x + cos²x = 1 for every x; Aryabhata's sine table and its radius of 3438; and the board question that loses a mark. Educational: CBSE class 11, Trigonometric Functions (unit circle, signs, sin²x + cos²x = 1). One to take with you: why is sin 30° exactly ½? Hint: turn the arrow up 30° and down 30°, and look at the string between them. Play along in your browser (free, nothing to install): https://nammaschool.github.io/interac... Or open it in Google Colab: https://colab.research.google.com/git... Chapters 0:00 The calculator's secret 0:40 Half a bowstring 1:41 The turning arrow 3:03 Below the axis 4:07 The arrow never changes length 5:48 What the examiner asks 7:11 The bowstring, again #trigonometry #unitcircle #sine #cbse #class11maths #mathhistory #nammaschool