Trigonometry, Sine theta and Our India

This post is for those who didn't know that Indians were the first to use trigonometry. You might have learnt trigonometry during you younger days probably in your high school or college. Has anyone thought about why is there a sine of an angle (sin theta)? Why is it sine and not something else? How did it get its name and many more unanswered questions...? (But if you already know then this article is not for you!).

Trigonometry began with the chords. A chord is a straight line drawn between any 2 points on a circle. Later trigonometry was based on a concept which is a slight modification of chords called sines. A sine of an angle is half the length of the chord of twice that angle (Is your head turning? Don't worry a picture describes a thousand words).

Here sine of angle DAB is half the length of the chord BE which is a chord to the angle BAE which is twice angle DAB. Does it make sense?

But why is it called sine and not something else? Well we need to go back to history to find out why... As sine of an angle is half the length of the chord of twice the angle as seen above, Indians basically astronomers who used trigonometry extensively used to call it ardh-jiya in Sanskrit. If you know Sanskrit then you know ardh means half and jiya is chord. They even started calling it as ardh-jiva. Arabs who were interested and amused by the concept of trigonometry took the knowledge of trigonometry from Indians and called it as jiba. Well they probably won't use vowels in their language so they renamed it as jb. After many years Latin translators thought the word jb was acronym for jaib. But jaib in Arabic meant breast. In Latin sinus had breast and bay as two of its meanings. English translators took this word sinus and adapted it as sine to depict half the length of the chord of twice the angle...

Well this was just how sine got its name.. But if you are really interested in learning all (at least fundamentals) about trigonometry i.e. cosine, tangent, cotangent, secant, cosecant ... then just go through the link. It's worth reading

http://www.clarku.edu/~djoyce/trig/