bonjour on donne [tex] \cos( \frac{2\pi}{5} ) = \frac{ \sqrt{5} - 1 }{4} [/tex] En déduire 1. [tex] \cos( - \frac { 2\pi}{5} ) [/tex] 2. [tex] \cos( \frac{3

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) .