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Exercice 16

(1)
\begin{align} \sin\left(\pi-\frac{\pi}{6}\right)=\sin\left(\frac{\pi}{6}\right)=\frac 1 2 \end{align}
(2)
\begin{align} \cos\left(\pi+\frac{\pi}{4}\right)=-\cos\left(\frac \pi 4\right)=-\frac{\sqrt{2}}{2} \end{align}

Exercice 17

On a $\sin\left(\frac\pi 3\right)=\frac{ \sqrt{3} }2$ et $\cos\left(\frac\pi 3\right)=\frac 1 2$.

a) $\sin\left(\frac{2\pi} 3\right)=\sin\left(\pi-\frac \pi 3\right)=\sin\left(\frac \pi 3\right)=\frac{\sqrt{3}}{2}$ et $\cos\left(\frac{2\pi} 3\right)=\cos\left(\pi-\frac \pi 3\right)=-\cos\left(\frac \pi 3\right)=-\frac{1}{2}$

b) $\sin\left(\frac{4\pi} 3\right)=\sin\left(\pi+\frac \pi 3\right)=-\sin\left(\frac \pi 3\right)=-\frac{\sqrt{3}}{2}$ et $\cos\left(\frac{4\pi} 3\right)=\cos\left(\pi+\frac \pi 3\right)=-\cos\left(\frac \pi 3\right)=-\frac{1}{2}$

Exercice 18

On a $\sin\left(\frac\pi 4\right)=\frac{ \sqrt{2} }2$ et $\cos\left(\frac\pi 4\right)=\frac { \sqrt{2} } 2$.

  1. $\sin\left(-\frac{\pi} 4\right)=-\sin\left(\frac \pi 4\right)=-\frac{\sqrt{2}}{2}$ et $\cos\left(-\frac{\pi} 4\right)=\cos\left(\frac \pi 4\right)=\frac{\sqrt{2}}{2}$
  2. $\sin\left(\frac{3\pi} 4\right)=\sin\left(\pi-\frac \pi 4\right)=\sin\left(\frac \pi 4\right)=\frac{\sqrt{2}}{2}$ et $\cos\left(\frac{3\pi} 4\right)=\cos\left(\pi-\frac \pi 4\right)=-\cos\left(\frac \pi 4\right)=-\frac{\sqrt{2}}{2}$
  3. $\sin\left(\frac{5\pi} 4\right)=\sin\left(\pi+\frac \pi 4\right)=-\sin\left(\frac \pi 4\right)=-\frac{\sqrt{2}}{2}$ et $\cos\left(\frac{5\pi} 4\right)=\cos\left(\pi+\frac \pi 4\right)=-\cos\left(\frac \pi 4\right)=-\frac{\sqrt{2}}{2}$
  4. $\sin\left(\frac{9\pi} 4\right)=\sin\left(2\pi+\frac \pi 4\right)=\sin\left(\frac \pi 4\right)=\frac{\sqrt{2}}{2}$ et $\cos\left(\frac{9\pi} 4\right)=\cos\left(2\pi+\frac \pi 4\right)=\cos\left(\frac \pi 4\right)=\frac{\sqrt{2}}{2}$
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