Question Number 215473 by alephnull last updated on 08/Jan/25
$${Solve}\:{for}\:{x} \\ $$$$ \\ $$$$\mathrm{2}{sin}^{\mathrm{2}} {x}+\mathrm{3}{sin}\left({x}\right)+\mathrm{1}=\mathrm{0}\:{for}\:\mathrm{0}\:\leqslant\:{x} \\ $$
Answered by Rasheed.Sindhi last updated on 08/Jan/25
$$\mathrm{2}{sin}^{\mathrm{2}} {x}+\mathrm{3}{sin}\left({x}\right)+\mathrm{1}=\mathrm{0} \\ $$$$\mathrm{2}{sin}^{\mathrm{2}} {x}+\mathrm{2}{sin}\left({x}\right)+{sin}\left({x}\right)+\mathrm{1}=\mathrm{0} \\ $$$$\mathrm{2}{sin}\left({x}\right)\left({sin}\left({x}\right)+\mathrm{1}\right)+\left({sin}\left({x}\right)+\mathrm{1}\right)=\mathrm{0} \\ $$$$\left({sin}\left({x}\right)+\mathrm{1}\right)\left(\mathrm{2}{sin}\left({x}\right)+\mathrm{1}\right)=\mathrm{0} \\ $$$${sin}\left({x}\right)=−\mathrm{1}\:\vee\:{sin}\left({x}\right)=−\frac{\mathrm{1}}{\mathrm{2}} \\ $$$${x}=\overset{×} {−\mathrm{90}},\overset{\checkmark} {\mathrm{270}}\:\vee\:{x}=\overset{×} {−\mathrm{30}},\overset{\checkmark} {\mathrm{330}} \\ $$
Commented by alephnull last updated on 08/Jan/25
$${thanks} \\ $$
Commented by mr W last updated on 08/Jan/25
$${x}=\mathrm{210}°\:{is}\:{also}\:{a}\:{solution}. \\ $$
Commented by Rasheed.Sindhi last updated on 08/Jan/25
$${Yes}\:{sir},\:{thanks}! \\ $$
Commented by alephnull last updated on 08/Jan/25
$$\mathrm{hello}\:\mathrm{mr}\:\mathrm{w} \\ $$
Commented by mr W last updated on 09/Jan/25
$${hello}\:{too}! \\ $$
Commented by Rasheed.Sindhi last updated on 09/Jan/25
$${sin}\left({x}\right)={sin}\left(\mathrm{180}−{x}\right) \\ $$$${sin}\left(−\mathrm{30}\right)={sin}\left(\mathrm{180}−\left(−\mathrm{30}\right)\right)={sin}\left(\mathrm{210}\right)=−\frac{\mathrm{1}}{\mathrm{2}} \\ $$