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Question Number 208377 by hardmath last updated on 14/Jun/24

$$\sin \mathrm{x}-\sin \frac{\pi }{6}>0$$$$\mathrm{x}=?$$

Commented by hardmath last updated on 14/Jun/24

$$$$Solve the inequality

Answered by lepuissantcedricjunior last updated on 14/Jun/24

$$\mathit{x}\mathit{e}\mathit{s}\mathit{t}\mathit{d}\mathit{e}\mathit{f}\mathit{i}\mathit{n}\mathit{i}\mathit{e}\mathit{d}\mathit{a}\mathit{n}\mathit{s}\mathit{q}\mathit{u}\mathit{o}\mathit{i}!$$$$\mathbb{R}\mathit{o}\mathit{u}]-2\mathit{\pi };2\mathit{\pi }]$$

Answered by mr W last updated on 14/Jun/24

$$\sin x>\sin \frac{\pi }{6}$$$$\Rightarrow 2k\pi +\frac{\pi }{6}<x<(2k+1)\pi -\frac{\pi }{6}$$

Commented by hardmath last updated on 14/Jun/24

$$\mathrm{thankyou}\mathrm{dear}\mathrm{professor}$$$$\frac{\pi }{6}+2\pi \mathrm{k}\mathrm{and}\frac{5\pi }{6}+2\pi \mathrm{k}?$$

Commented by mr W last updated on 14/Jun/24

$$isthisnotthesameasisaid?$$$$\frac{5\pi }{6}=\pi -\frac{\pi }{6}!$$

Commented by hardmath last updated on 14/Jun/24

$$\mathrm{Dear}\mathrm{professor},$$$$\mathrm{k}=0\Rightarrow \pi -\frac{\pi }{6}=\frac{5\pi }{6}?$$

Commented by mr W last updated on 14/Jun/24

$$yes$$

Commented by hardmath last updated on 14/Jun/24

$$\mathrm{thankyou}\mathrm{dear}\mathrm{professor}$$

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