Question and Answers Forum

All Questions      Topic List

Algebra Questions

Previous in All Question      Next in All Question      

Previous in Algebra      Next in Algebra      

Question Number 87737 by M±th+et£s last updated on 05/Apr/20

$$solve$$$$sin\left(\frac{\pi }{\left[\frac{\left[x\right]}{4}\right]}\right)=\frac{1}{2}$$

Answered by mahdi last updated on 06/Apr/20

$$\mathrm{u}=\left[\frac{\left[\mathrm{x}\right]}{4}\right]\Rightarrow -1⩽\frac{1}{\mathrm{u}}⩽1\Rightarrow -\pi ⩽\frac{\pi }{\mathrm{u}}⩽\pi \{\mathrm{u}\ne 0\Rightarrow \mathrm{x}\notin [0,4)\}$$$$\sin \left(\frac{\pi }{\mathrm{u}}\right)=\frac{1}{2}\Rightarrow \{\begin{array}{l}\frac{\pi }{\mathrm{u}}=\frac{\pi }{6}+2\mathrm{k}\pi \\ \frac{\pi }{\mathrm{u}}=\frac{5\pi }{6}+2\mathrm{k}\pi \end{array}$$$$-\pi ⩽\frac{\pi }{\mathrm{u}}⩽\pi \Rightarrow \frac{\pi }{\mathrm{u}}=\frac{\pi }{6}\vee \frac{5\pi }{6}$$$$\mathrm{u}=6\vee \frac{6}{5}\stackrel{\mathrm{u}\in \mathrm{Z}}{\Rightarrow }\mathrm{u}=6$$$$\left[\frac{\left[\mathrm{x}\right]}{4}\right]=6\Rightarrow 24⩽\mathrm{x}<28$$

Commented by M±th+et£s last updated on 05/Apr/20

$$godblessyousir$$

Commented by M±th+et£s last updated on 06/Apr/20

$$sirif-24⩽x<-20\to \to x=-0.5not1$$$$soS\{24⩽x<8\}$$

Commented by mahdi last updated on 06/Apr/20

$$\mathrm{what}?\mathrm{how}[-24⩽\mathrm{x}<-20\Rightarrow \mathrm{x}=-0.5]?$$

Commented by M±th+et£s last updated on 06/Apr/20

$$sorryimeanans=-0.5if-24⩽x<20$$

Commented by M±th+et£s last updated on 06/Apr/20

Commented by mahdi last updated on 06/Apr/20

$$\mathrm{ok}\mathrm{ser},\mathrm{i}\mathrm{sorry}.\{\begin{array}{l}\frac{\pi }{6}+2\mathrm{k}\pi \Rightarrow ...,\frac{-11\pi }{6},\frac{\pi }{6},\frac{13\pi }{6},...\\ \frac{5\pi }{6}+2\mathrm{k}\pi \Rightarrow ...,\frac{-7\pi }{6},\frac{5\pi }{6},\frac{17\pi }{6},...\end{array}$$$$\mathrm{only}:\frac{\pi }{6}\mathrm{and}\frac{5\pi }{6}\in [-1,1]$$

Commented by M±th+et£s last updated on 06/Apr/20

$$thankyousir$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com