Functions of Sums and Related Functions

This chapter discusses functions of sums and related functions in application of the trigonometric functions. The function of sums has three sets of relations, namely, sines and cosines of sums and differences, functions of a negative angle, and cofunction relations. Because sin (90° − β) is equal to the cosine of the complementary angle β, cosine is the complementary function of the sine or the cofunction. Thus, the sine and cosine are called cofunctions. Similarly, the tangent and cotangent are cofunctions. The functions of sums relations are called reduction formulas because in each case the left member is a function of the sum of angles while the right member contains only functions of single angles. This chapter also discusses the sum to product formulas and product to sum formulas.