Solve-for-x-2sin-2-x-3sin-x-1-0-for-0-x-

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

2sin^2 x+3sin(x)+1=0 2sin^2 x+2sin(x)+sin(x)+1=0 2sin(x)(sin(x)+1)+(sin(x)+1)=0 (sin(x)+1)(2sin(x)+1)=0 sin(x)=−1 ∨ sin(x)=−(1/2) x=−90^(×) ,270^(✓) ∨ x=−30^(×) ,330^(✓)

$$\mathrm{2}{sin}^{\mathrm{2}} {x}+\mathrm{3}{sin}\left({x}\right)+\mathrm{1}=\mathrm{0} \\ $$$$\mathrm{2}{sin}^{\mathrm{2}} {x}+\mathrm{2}{sin}\left({x}\right)+{sin}\left({x}\right)+\mathrm{1}=\mathrm{0} \\ $$$$\mathrm{2}{sin}\left({x}\right)\left({sin}\left({x}\right)+\mathrm{1}\right)+\left({sin}\left({x}\right)+\mathrm{1}\right)=\mathrm{0} \\ $$$$\left({sin}\left({x}\right)+\mathrm{1}\right)\left(\mathrm{2}{sin}\left({x}\right)+\mathrm{1}\right)=\mathrm{0} \\ $$$${sin}\left({x}\right)=−\mathrm{1}\:\vee\:{sin}\left({x}\right)=−\frac{\mathrm{1}}{\mathrm{2}} \\ $$$${x}=\overset{×} {−\mathrm{90}},\overset{\checkmark} {\mathrm{270}}\:\vee\:{x}=\overset{×} {−\mathrm{30}},\overset{\checkmark} {\mathrm{330}} \\ $$

Commented by alephnull last updated on 08/Jan/25