Introduction to Trigonometry
Trigonometry is the study of relationships between the sides and angles of a triangle. Ratio of the sides of a right triangle with respect to its acute angle is called trigonometric ratio of the angle.
Identities involving trigonometric ratios are called trigonometric identities. The reciprocals of the ratios sin A, cos A and tan A are cosec A, sec A and cot A respectively.
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.
The values of the trigonometric ratios of an angle do not vary with the lengths of the sides of the triangle, if the angle remains the same. An equation involving trigonometric ratios of an angle is called a trigonometric identity, if it is true for all values of the angle(s) involved.
If one of the trigonometric ratios of an acute angle is known, the remaining trigonometric ratios of the angle can be determined. The value of sin A or cos A lie in the closed interval [–1, 1]. As the angle A increases from 0° to 90°, sin A increases from 0 to 1 and cos A decreases from 1 to 0.
Sine, cosine, tangent, Trigonometric Ratios of Complementary Angles