Bonjour,
Ex 1)
mesure principale = mesure comprise dans [-π;π]
-5π/4 = -π/4 - 4π/4 = -π4/ - π donc -π/4
1000π = 0 + 500x2π donc 0
500π/3 = 2π/3 + 498π/3 = 2π/3 + 166π donc 2π/3
2015π/4 = -π/4 + 2016π/4 = -π/4 + 504π donc -π/4
5π/3 = -π/3 + 6π/3 = -π/3 + 2π donc -π/3
-3π = -π - 2π donc -π
-31π/6 = 5π/6 - 36π/6 = 5π/6 - 6π donc 5π/6
Ex 2)
1) a)
15° = 2π/360 x 15 = 30π/360 = π/12
200° = 2π/360 x 200 = 400π/360 = 10π/9
210° = 2π/360 x 210 = 420π/360 = 7π/6
b)
75° = 2π/360 x 75 = 75π/180 = 5π/12
29° = 2π/360 x 29 = 29π/180
1° = π/180
2) π/4 = 180/4 ° = 45°
pi/5 = 180/5 ° = 36°
7π/18 = 7x180/18 ° = 70°
b) 3 rad = (180/π) x 3 = 540/π °
1 rad = 180/π °
7/144 rad = 7/144 x 180/π ° = 7 x 15//12π ° = 35/4π °
