Exercice : Mesure Principale 6

Donner la mesure en degré de chacun des angles :

Question

\(\frac{\pi}{5}\) radians

Indice

\(2\pi \mapsto360\)

Solution

\(2\pi \mapsto360\)

\(\frac{\pi}{5} \mapsto \frac{360}{2\pi} \times \frac{\pi}{5}\)

\(\iff \frac{\pi}{5} \mapsto \frac{360}{10}=36\)

Question

\(\frac{3\pi}{4}\) radians

Indice

\(2\pi \mapsto360\)

Solution

\(2\pi \mapsto360\)

\(\frac{3\pi}{4} \mapsto \frac{360}{2\pi} \times \frac{3\pi}{4}\)

\(\iff \frac{3\pi}{4} \mapsto \frac{360\times 3}{8}=45\times 3=135\)

Question

\(\frac{5\pi}{3}\) radians

Indice

\(2\pi \mapsto360\)

Solution

\(2\pi \mapsto360\)

\(\frac{5\pi}{3} \mapsto \frac{360}{2\pi} \times \frac{5\pi}{3}\)

\(\iff \frac{5\pi}{3} \mapsto \frac{360\times 5}{6}=60 \times 5=300\)

Question

\(\frac{\pi}{12}\) radians

Indice

\(2\pi \mapsto360\)

Solution

\(2\pi \mapsto360\)

\(\frac{\pi}{12} \mapsto \frac{360}{2\pi} \times \frac{\pi}{12}\)

\(\iff \frac{\pi}{12} \mapsto \frac{360}{24}=15\)