Résoudre des équations et inéquations trigonométriques - TS - Exercice Mathématiques

Quelles sont les solutions de l'équation \(\displaystyle{2\left(sinx\right)^2-2 = 0}\) sur \(\displaystyle{\left[ 0 ; 2\pi \right]}\) ?

\(\displaystyle{S = \left\{ -\dfrac{\pi}{2} ;\dfrac{\pi}{2} \right\}}\)

\(\displaystyle{S = \left\{ -\dfrac{\pi}{2} ;0 ;\dfrac{\pi}{2} \right\}}\)

\(\displaystyle{S = \left\{ 0;\dfrac{\pi}{2} ;\dfrac{3\pi}{2} \right\}}\)

\(\displaystyle{S = \left\{ \dfrac{\pi}{2} ;\dfrac{3\pi}{2} \right\}}\)

Quelles sont les solutions de l'équation \(\displaystyle{\left(\cos x\right)^2-\cos x +\dfrac{1}{4}= 0}\) sur \(\displaystyle{\left[ -\pi ; \pi \right[}\) ?

\(\displaystyle{S = \left\{-\dfrac{\pi}{6};\dfrac{\pi}{6} \right\}}\)

\(\displaystyle{S = \left\{-\dfrac{\pi}{2} ;-\dfrac{\pi}{6}; \dfrac{\pi}{6}; \dfrac{\pi}{2} \right\}}\)

\(\displaystyle{S = \left\{-\dfrac{\pi}{3} ;\dfrac{\pi}{3}\right\}}\)

\(\displaystyle{S = \left\{ \dfrac{\pi}{2} ;\dfrac{3\pi}{2} \right\}}\)

Quelles sont les solutions de l'équation \(\displaystyle{\cos \left(\dfrac{\pi}{2}+x\right)= \sin x}\) sur \(\displaystyle{\left[ 0 ; 2\pi \right[}\) ?

\(\displaystyle{S = \left\{ 0 ;\dfrac{\pi}{2}; \pi \right\}}\)

\(\displaystyle{S = \left\{0 ;\pi; 2\pi \right\}}\)

\(\displaystyle{S = \left\{0 ;\pi\right\}}\)

\(\displaystyle{S = \left\{ \dfrac{\pi}{2} ;\dfrac{3\pi}{2} \right\}}\)

Quelles sont les solutions de l'équation \(\displaystyle{\sin\left( x-\dfrac{\pi}{3}\right) = \dfrac{\sqrt2}{2}}\) sur \(\displaystyle{\left[ -\pi ; \pi \right]}\) ?

\(\displaystyle{S = \left\{ -\dfrac{11\pi}{12} ; \dfrac{7\pi}{12} \right\}}\)

\(\displaystyle{S = \left\{ \dfrac{7\pi}{12} ; \dfrac{13\pi}{12}\right\}}\)

\(\displaystyle{S = \left\{ -\dfrac{11\pi}{12} ; - \dfrac{\pi}{6}; \dfrac{7\pi}{12} \right\}}\)

\(\displaystyle{S = \left\{ \dfrac{7\pi}{12} \right\}}\)

Déterminer les solutions de l'équation \(\displaystyle{2 \cos \left(3x\right) -1 =0}\) dans \(\displaystyle{\left[ 0 ; 2\pi \right[}\).

\(\displaystyle{S = \left\{ \dfrac{\pi}{9}; \dfrac{5\pi}{9} ; \dfrac{7\pi}{9} ; \dfrac{11\pi}{9} ; \dfrac{13\pi}{9} ; \dfrac{17\pi}{9} \right\}}\)

\(\displaystyle{S = \left\{ \dfrac{\pi}{9}; \dfrac{7\pi}{9} ; \dfrac{13\pi}{9}\right\}}\)

\(\displaystyle{S = \left\{ \dfrac{\pi}{9}; \dfrac{5\pi}{9} ; \dfrac{10\pi}{9} ; \dfrac{14\pi}{9} \right\}}\)

\(\displaystyle{S = \left\{ \dfrac{\pi}{18}; \dfrac{5\pi}{18} ; \dfrac{7\pi}{18} ; \dfrac{11\pi}{18} ; \dfrac{13\pi}{18} ; \dfrac{17\pi}{18} \right\}}\)

Déterminer les solutions de l'équation \(\displaystyle{2\sin\left(2x+\pi\right)-1 = 0}\) dans \(\displaystyle{\left[ 0 ; 2\pi \right[}\).

\(\displaystyle{S = \left\{ \dfrac{7\pi}{12}; \dfrac{11\pi}{12} ;\dfrac{19\pi}{12} ; \dfrac{23\pi}{12} \right\}}\)

\(\displaystyle{S = \left\{ \dfrac{\pi}{12}; \dfrac{5\pi}{12} ;\dfrac{13\pi}{12} ; \dfrac{17\pi}{12} \right\}}\)

\(\displaystyle{S = \left\{ \dfrac{7\pi}{12}; \dfrac{11\pi}{12} \right\}}\)

\(\displaystyle{S = \left\{\dfrac{5\pi}{12} ; \dfrac{17\pi}{12} \right\}}\)

Déterminer les solutions de l'équation \(\displaystyle{\cos\left(2x\right) = \sin\left(x\right)}\) dans \(\displaystyle{\left[ 0 ; 2\pi \right[}\).

\(\displaystyle{S = \left\{ \dfrac{\pi}{6}; \dfrac{5\pi}{6} ;\dfrac{3\pi}{2} \right\}}\)

\(\displaystyle{S = \left\{ \dfrac{\pi}{4}; \dfrac{5\pi}{4} \right\}}\)

\(\displaystyle{S = \left\{ \dfrac{\pi}{6} ;\dfrac{3\pi}{2} \right\}}\)

\(\displaystyle{S = \left\{ \dfrac{\pi}{6}; \dfrac{\pi}{2} ;\dfrac{3\pi}{2} \right\}}\)

Déterminer les solutions de l'équation \(\displaystyle{\left(cosx\right)^2 -\dfrac{1}{2}\cos x-\dfrac{1}{2}=0}\) dans \(\displaystyle{\left[ 0 ; 2\pi \right[}\).

\(\displaystyle{S = \left\{ 0;\dfrac{2\pi}{3}; \dfrac{4\pi}{3}\right\}}\)

\(\displaystyle{S = \left\{ -\dfrac{2\pi}{3};0;\dfrac{2\pi}{3}\right\}}\)

\(\displaystyle{S = \left\{\dfrac{2\pi}{3} ;\Pi;\dfrac{4\pi}{3}\right\}}\)

\(\displaystyle{S = \left\{\dfrac{2\pi}{3} ;1;\dfrac{4\pi}{3}\right\}}\)

Résoudre des équations et inéquations trigonométriques Exercice

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