II - Trigonometric Functions of Angles

Abstract

This chapter provides an overview on trigonometric functions of angles. The angles relative to a rectangular coordinate system can be placed with their vertices at the origin and their initial sides along the positive x-axis. These angles are in a standard position. Angles measured in a counter-clockwise direction are to be taken as positive whereas angles measured in a clockwise direction are negative. The trigonometric functions are defined as ratios of real numbers and hence, are real numbers. All of the ratios may be positive or negative and that some may be zero or undefined. The ratios depend solely on θ and not on the position of the point on the terminal side of θ. The six trigonometric functions are not independent. The reciprocal functions, the tangent and cotangent relations, and the Pythagorean relations are true for all values of θ for which each member is defined and hence are called trigonometric identities. Any of the trigonometric functions can be expressed in terms of series expansions. Using these series expansions, it is possible to obtain approximations of the trigonometric functions of any angle to any desired accuracy.