✅ Corrigé détaillé — Exercice 1
Partie A
1) Degrés → radians (× π/180) :
a) 90° → π/2. b) 270° → 3π/2. c) 150° → 5π/6. d) 240° → 4π/3. e) 315° → 7π/4.
2) Radians → degrés (× 180/π) :
a) π/4 → 45°. b) 5π/6 → 150°. c) 4π/3 → 240°. d) 7π/4 → 315°. e) 11π/6 → 330°.
Partie B
| Expression | Valeur exacte |
|---|---|
| a) cos(π/3) | 1/2 |
| b) sin(π/6) | 1/2 |
| c) cos(π/4) | √2/2 |
| d) sin(π/2) | 1 |
| e) cos(π) | −1 |
| f) sin(0) | 0 |
Partie C
4) cos²(x) + sin²(x) = 1 → cos²(x) = 1 − (3/5)² = 1 − 9/25 = 16/25.
x ∈ [0 ; π/2] → cos(x) ≥ 0 → cos(x) = 4/5.
5) cos²(x) + sin²(x) = 1 → sin²(x) = 1 − 3/4 = 1/4.
x ∈ [π/2 ; π] → sin(x) ≥ 0 → sin(x) = 1/2.
Vérification : sin(x) = 1/2 et cos(x) = −√3/2 → c’est l’image de 5π/6. ✓