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Question Number 215473 by alephnull last updated on 08/Jan/25

$$Solveforx$$$$$$$$2{sin}^{2}x+3sin\left(x\right)+1=0for0⩽x$$

Answered by Rasheed.Sindhi last updated on 08/Jan/25

$$2{sin}^{2}x+3sin\left(x\right)+1=0$$$$2{sin}^{2}x+2sin\left(x\right)+sin\left(x\right)+1=0$$$$2sin\left(x\right)(sin\left(x\right)+1)+(sin\left(x\right)+1)=0$$$$(sin\left(x\right)+1)(2sin\left(x\right)+1)=0$$$$sin\left(x\right)=-1\vee sin\left(x\right)=-\frac{1}{2}$$$$x=\stackrel{\times }{-90},\check{270}\vee x=\stackrel{\times }{-30},\check{330}$$

Commented by alephnull last updated on 08/Jan/25

$$thanks$$

Commented by mr W last updated on 08/Jan/25

$$x=210°isalsoasolution.$$

Commented by Rasheed.Sindhi last updated on 08/Jan/25

$$Yessir,thanks!$$

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

$$hellotoo!$$

Commented by Rasheed.Sindhi last updated on 09/Jan/25

$$sin\left(x\right)=sin(180-x)$$$$sin(-30)=sin(180-(-30))=sin\left(210\right)=-\frac{1}{2}$$

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