Exercice : Mesure Principale 7

Donner la mesure en radians de chacun des angles :

Question

72°

Indice

\(360 \mapsto 2\pi\)

Solution

\(360 \mapsto 2\pi\)

\(72 \mapsto \frac{2\pi}{360}\times 72\)

\(\iff 72 \mapsto \frac{2\pi}{10} \times 2\)

\(\iff 72 \mapsto \frac{2\pi}{5}\)

Question

105°

Indice

\(360 \mapsto 2\pi\)

Solution

\(360 \mapsto 2\pi\)

\(105 \mapsto \frac{2\pi}{360}\times 105\)

\(\iff 105 \mapsto \frac{210\pi}{360}\)

\(\iff 105 \mapsto \frac{21\pi}{36}\)

\(\iff 105 \mapsto \frac{7\pi}{12}\)

Question

20°

Indice

\(360 \mapsto 2\pi\)

Solution

\(360 \mapsto 2\pi\)

\(20 \mapsto \frac{2\pi}{360}\times 20\)

\(\iff 20 \mapsto \frac{2\pi}{36} \times 2\)

\(\iff 20 \mapsto \frac{\pi}{18} \times 2\)

\(\iff 20 \mapsto \frac{\pi}{9}\)

Question

Indice

\(360 \mapsto 2\pi\)

Solution

\(360 \mapsto 2\pi\)

\(9 \mapsto \frac{2\pi}{360}\times 9\)

\(\iff 9 \mapsto \frac{2\pi}{40}\)

\(\iff 9 \mapsto \frac{\pi}{20}\)

Question

30°

Indice

\(360 \mapsto 2\pi\)

Solution

\(360 \mapsto 2\pi\)

\(30 \mapsto \frac{2\pi \times 30}{360}=\frac{60\pi}{360}=\frac{\pi}{60}\)

Question

-45°

Indice

\(360 \mapsto 2\pi\)

Solution

\(360 \mapsto 2\pi\)

\(-45 \mapsto \frac{2\pi \times (-45)}{360}=\frac{-90\pi}{360}=\frac{-\pi}{4}\)