Question

cos (23pi/12)*sin(pi/12)=?
Se poate explica mai detaliat? Am gasit o rezolvare dar nu inteleg de ce se parcurge asa

Answer 1

cos(23π/12)*sin(π/12)= ?

cos(23π/12)=cos (-23π/12) deoarece cosx, functie para=

=cos (2π-23π/12) deoarecfe cos x, functie periodica , avand periopada principala 2π ,deci cos (2π+α)=cos α

cos (2π-23π/12)=cos(π/12)., deoarece 2π-23π/12=24π/12-23π/12

Deci

cos(23π/12)*sin(π/12)= cos(π/12)sin (π/12)= (1/2) * 2cos(π/12)*sin(π/12)=(1/2)sinπ/6, deoarece 2sinxcosx=sin2x si deoarece 1=2/2, artificiu de calcul

deci (1/2)sin(π/6)=(1/2) *(1/2)=1/4

as simple as that!!!