Question

Fie a∈(π,3π/2) astfel incat sin a = -4/5 . Calculati tg a/2 .

Answer 1

sin a=-4/5
sin²a+cos²a=1
cos²a=1-sin²a
cos²a=1-(-4/5)²
cos²a=1-16/25
cos²a=(25-16)/25
cos²a=9/25
a∈(π;3π/2) valoarea cosinusului este negativa
cos a=-3/5
tg a/2=1-cos a/sin a=1-(-3/5)/(-4/5)=(1+3/5)/(-4/5)=8/5*(-5/4)=8*(-5)/5*4=-40/20=-2