The relation between sines and chords

In this section we'll only consider sines of angles between 0° and 90°. In the section on trigonometric functions, we'll define sines for arbitrary angles.
A sine is half of a chord. More accurately, the sine of an angle is half the chord of twice the angle.

The bow and arrow diagram
Consider the angle BAD in this figure, and assume that AB is of unit length. Let the point C be the foot of the perpendicular dropped from B to the line AD. Then the sine of angle BAD is defined to be the length of the line BC, and it is written sin BAD. You can double the angle BAD to get the angle BAE, and the chord of angle BAE is BE. Thus, the sine BC of angle BAD is half the chord BE of angle BAE, while the angle BAE is twice the angle BAD. Therefore, as stated before, the sine of an angle is half the chord of twice the angle.
The point of this is just to show that sines are all that difficult to understand. (Whoops, that's a slip! I meant to write "not all that difficult to understand.")
The meaning of the word "sine"The Sanskrit word for chord-half was jya-ardha, which was sometimes shortened to jiva. This was brought into Arabic as jiba, and written in Arabic simply with two consonants jb, vowels not being written. Later, Latin translators selected the word sinus to translate jb thinking that the word was an arabic word jaib, which meant breast, and sinus had breast and bay as two of its meanings. In English, sinus was imported as "sine".
This word history for "sine" is interesting because it follows the path of trigonometry from India, through the Arabic language from Baghdad through Spain, into western Europe in the Latin language, and then to modern languages such as English.