2 ESERCIZI Equazioni e disequazioni goniometriche 299 2senx sen2x > 0 [0 + 2k 2cosx [ 2 + 2k 0 _ _ _5_ _ _ _3_ [ 6 + 2k cos2x _ _ _ _ [ 6 + k 0 [ 8 + 2k 0 2 cosx + 1 _ _ _3_ _ _ [0 + 2k 0 _ _ [0 + 2k < x < + 2k ; con x 2 + 2k ] senx _3_ 314 cos2x sen2x 0 _ 2 2 316 senx cos x _ _ [ 8 + k x 8 + k ] 2 3 315 sen __ x + ___ <___ 12) _5_ [0 + 2k < x < 4 + 2k ; 4 + 2k < x < 2 + 2k ] sen2x 312 ________ 0 (2 _ _ 13 _4_ _4_ ___ _4_ [ 9 + 3 k < x < 9 + 3 k ] _ 5 1 arcsen _______ [ ( 2 ) _ 5 1 +2k x arcsen _______ ( 2 ) + 2k ] PRACTICE WITH CLIL Werner formulas In addition to the goniometric formulas that we have learnt in this unit, there are others called Werner formulas, which Johannes Werner (1468-1528), an astronomer and mathematician, used to simplify astronomical calculations. In fact, the determination of astronomical quantities involves very large numbers and, since the current tools were not available at the time, it was necessary to use particular strategies to perform calculations with these numbers. These formulas make it possible to transform the multiplication of two very large numbers into the sum of two other numbers using the calculation of cosines. Indeed, Werner formulas transform the calculation of the product of goniometric functions of different arguments into sums or differences of goniometric functions. In a nutshell, they transform a multiplicative goniometric expression into another additive. 115

PRACTICE WITH CLIL