Exercices corrigés — Trigonométrie (1ère STI2D)

\[ 60^\circ=\frac{60\pi}{180}=\frac{\pi}{3} \]

\[ \boxed{\frac{\pi}{3}} \]

\[ \frac{\pi}{4}=45^\circ \]

\[ \boxed{45^\circ} \]

\[ \cos\left(\frac{\pi}{3}\right)=\frac{1}{2} \]

\[ \boxed{\frac{1}{2}} \]

\[ \sin\left(\frac{\pi}{6}\right)=\frac{1}{2} \]

\[ \boxed{\frac{1}{2}} \]

\[ M(\cos x;\sin x) \]

\[ \cos(-x)=\cos x \]

\[ \boxed{\cos x} \]

\[ \sin(-x)=-\sin x \]

\[ \boxed{-\sin x} \]

\[ \cos(x+2\pi)=\cos x \]

\[ \boxed{\cos x} \]

\[ \sin(x+2\pi)=\sin x \]

\[ \boxed{\sin x} \]

\[ \cos\left(\frac{13\pi}{6}\right)=\cos\left(2\pi+\frac{\pi}{6}\right)=\cos\left(\frac{\pi}{6}\right) \] \[ =\frac{\sqrt{3}}{2} \]

\[ \boxed{\frac{\sqrt{3}}{2}} \]

\[ \sin(\pi)=0 \]

\[ \boxed{0} \]

(a) \[ 90^\circ=\frac{\pi}{2} \]

(b) \[ \cos\left(\frac{\pi}{2}\right)=0 \]

(c) \[ \sin(-x)=-\sin x \]

\[ \boxed{90^\circ=\frac{\pi}{2},\quad \cos\left(\frac{\pi}{2}\right)=0,\quad \sin(-x)=-\sin x} \]