Few teachers in the world ever teach the “sine” function as defined originally by the angle (θ = 1 radian) formed by the chord (弦) of length 1 in an unit circle ( of radius 1).
Chinese truthfully translated in the original definition as shown in the picture.
sin 正弦: “Right Chord”
cos 馀弦 “Remaining Chord”
tan 正切 “Right Cut”:
Dr. Yeo Ning Hong was the former cabinet Minister of Singapore. He wrote a few Math books after retirement to teach his grand-daughters in primary schools – on Trigonometric Identity Proofs !!!
He has wonderful tricks to make such difficult Secondary 3 Math easy for kids, and of course, also helps the weak Math teenagers.
Trig Or Treat: An Encyclopedia of Trigonometric Identity Proofs With Intellectually Challenging Games
The other books by him are:
The Pleasures of Pi,e and Other Interesting Numbers
tan α +tan β +tan γ = tan α.tan β.tan γ
What is “sin A” concretely ?
1. Draw a circle (diameter 1)
2. Connect any 3 points on the circle to form a triangle of angles A, B, C.
3. The length of sides opposite A, B, C are sin A, sin B, sin C, respectively.
By Sine Rule:
where sides a,b,c opposite angles A, B, C respectively.
a = sin A
b = sin B
c = sin C