means curve, when the Arabic version was translated into Latin. Soon the word sinus , also used as sine , became common in mathematical texts throughout Europe. An English Professor of astronomy Edmund Gunter ( – ), first used the abbreviated notation ‘ sin ’. The origin of the terms ‘cosine’ and ‘tangent’ was much later.
The cosine function arose from the need to compute the sine of the complementary angle. Aryabhatta called it kotijya . The name cosinus originated with Edmund Gunter. In , the English Mathematician Sir Jonas Moore first used the abbreviated notation ‘ cos ’ .
Remark : Note that the symbol sin A is used as an abbreviation for ‘the sine of the angle A’. sin A is not the product of ‘sin’ and A. ‘sin’ separated from A has no meaning. Similarly, cos A is not the product of ‘cos’ and A.
Similar interpretations follow for other trigonometric ratios also. Now, if we take a point P on the hypotenuse AC or a point Q on AC extended, of the right triangle ABC and draw PM perpendicular to AB and QN perpendicular to AB extended (see Fig. . ), how will the trigonometric ratios of A in PAM differ from those of A in CAB or from those of A in QAN?
To answer this, first look at these triangles. Is PAM similar to CAB? From Chapter , recall the AA similarity criterion. Using the criterion, you will see that the triangles PAM and CAB are similar.
Therefore, by the property of similar triangles, the corresponding sides of the triangles are proportional. So, we have AM AB = AP MP Aryabhata C.E. – Fig. .
From this, we find MP AP = BC AC . Similarly, AM AP = cos A, MP tan A AM and so on. This shows that the trigonometric ratios of angle A in PAM not differ from those of angle A in CAB. In the same way, you should check that the value of sin A (and