Question Number 208377 by hardmath last updated on 14/Jun/24
$$\mathrm{sin}\:\mathrm{x}\:−\:\mathrm{sin}\:\frac{\pi}{\mathrm{6}}\:>\:\mathrm{0} \\ $$$$\mathrm{x}\:=\:? \\ $$
Commented by hardmath last updated on 14/Jun/24
$$ \\ $$Solve the inequality
Answered by lepuissantcedricjunior last updated on 14/Jun/24
![x est definie dans quoi! R ou ]−2𝛑;2𝛑]](Q208378.png)
$$\boldsymbol{{x}}\:\boldsymbol{{est}}\:\boldsymbol{{definie}}\:\boldsymbol{{dans}}\:\boldsymbol{{quoi}}! \\ $$$$\left.\mathbb{R}\left.\:\boldsymbol{{ou}}\:\right]−\mathrm{2}\boldsymbol{\pi};\mathrm{2}\boldsymbol{\pi}\right] \\ $$
Answered by mr W last updated on 14/Jun/24
$$\mathrm{sin}\:{x}\:>\:\mathrm{sin}\:\frac{\pi}{\mathrm{6}} \\ $$$$\Rightarrow\mathrm{2}{k}\pi+\frac{\pi}{\mathrm{6}}<{x}<\left(\mathrm{2}{k}+\mathrm{1}\right)\pi−\frac{\pi}{\mathrm{6}} \\ $$
Commented by hardmath last updated on 14/Jun/24
$$\mathrm{thankyou}\:\mathrm{dear}\:\mathrm{professor} \\ $$$$\frac{\pi}{\mathrm{6}}\:+\mathrm{2}\pi\mathrm{k}\:\:\:\mathrm{and}\:\:\:\frac{\mathrm{5}\pi}{\mathrm{6}}\:+\:\mathrm{2}\pi\mathrm{k}\:? \\ $$
Commented by mr W last updated on 14/Jun/24
$${is}\:{this}\:{not}\:{the}\:{same}\:{as}\:{i}\:{said}? \\ $$$$\frac{\mathrm{5}\pi}{\mathrm{6}}=\pi−\frac{\pi}{\mathrm{6}}\:! \\ $$
Commented by hardmath last updated on 14/Jun/24
$$\mathrm{Dear}\:\mathrm{professor}, \\ $$$$\mathrm{k}\:=\:\mathrm{0}\:\Rightarrow\:\pi\:−\:\frac{\pi}{\mathrm{6}}\:=\:\frac{\mathrm{5}\pi}{\mathrm{6}}\:? \\ $$
Commented by mr W last updated on 14/Jun/24
$${yes} \\ $$
Commented by hardmath last updated on 14/Jun/24
$$\mathrm{thankyou}\:\mathrm{dear}\:\mathrm{professor} \\ $$