is the hypotenuse of the right triangle and the side AB is a part of A. So, we call it the side adjacent to angle A. Fig. .
Fig. . Note that the position of sides change when you consider angle C in place of A (see Fig. .
). You have studied the concept of ‘ratio’ in your earlier classes. We now define certain ratios involving the sides of a right triangle, and call them trigonometric ratios. The trigonometric ratios of the angle A in right triangle ABC (see Fig.
. ) are defined as follows : sine of A = side opposite to angle A cosine of A = side adjacent to angle A tangent of A = side opposite to angle A side adjacent to angle A cosecant of A = sine of A side opposite to angle A secant of A = cosine of A side adjacent to angle A cotangent of A = side adjacent to angle A tangent of A side opposite to angle A The ratios defined above are abbreviated as sin A, cos A, tan A, cosec A, sec A and cot A respectively. Note that the ratios cosec A, sec A and cot A are respectively, the reciprocals of the ratios sin A, cos A and tan A. Also, observe that tan A = and cot A = cosA .
So, the trigonometric ratios of an acute angle in a right triangle express the relationship between the angle and the length of its sides. Why don’t you try to define the trigonometric ratios for angle C in the right triangle? (See Fig. .
) Fig. . The first use of the idea of ‘sine’ in the way we use it today was in the work Aryabhatiyam by Aryabhata, in A.D. .
Aryabhata used the word ardha-jya for the half-chord, which was shortened to jya or jiva in due course. When the Aryabhatiyam was translated into Arabic, the word jiva was retained as it is. The word jiva was translated into sinus, which