Sine of an Angle

Sine of an Angle

The sine of an angle is the y-coordinate of the corresponding point P on the unit circle (which has a radius of 1).

When any real number is associated with the sine of an angle whose measure in the unit circle is that number, a circular function called a sine function is defined.

Graphical representation of the function $$f(x)= sin(x)$$, which has an amplitude of 1 and a period of 2π.

Educational note

The argument of sine is a number (that is, the measure of an angle or an angle of rotation), not the geometric figure itself (angle). Therefore, the expression “sine of an angle” is a shortened version of “the sine of the measure of an angle”.

Etymologycal note

The term “sine” is derived from the Latin sinus meaning “bending”, “curve”, or “hollow”. In human anatomy, the term sinus refers to various cavities such as the carotid sinus, facial sinuses, venous sinuses and pilonidal sinuses (wounds). The term “sine” was introduced into mathematics through transcriptions from one language into another. Although the study of trigonometric ratios in right triangles or circles goes back to ancient Greece (around 400 BCE), the most important work on the subject was done by the Indian mathematician Ăryabhata who used the term jya, meaning “chord”, to refer to the half-chord that subtends an arc. The term was adopted and translated by Arab mathematicians as jb (pronounced ja-ib) which means “chord”, but also “breast”. European mathematicians, in turn, translated the Arabic texts into Latin, and the word jb became sinus, which means “curve” or “hollow”.