Verified answer

Réponse :

Explications étape par étape

cos(2π/5) = cos72° ≈ 0,309 .

cos(-2π/5) = cos(2π/5) .

cos(3π/5) = cos(5π/5 - 2π/5) =  -cos(2π/5) .

cos(-3π/5) = -cos(2π/5) .

sin²(3π/5) = 16/16 - (5-2√5+1)/16

                = 16/16 - (6-2√5)/16

                = (10+2√5)/16

                = (5+√5)/8

donc sin(3π/5) = 0,5*√[(5+√5)/2] ≈ 0,951 .

cos(7π/5) = cos(π + 2π/5) = -cos(2π/5) .

sin(2π/5) = sin(π - 3π/5) = sin(3π/5) .