Question and Answers Forum

All Questions      Topic List

Trigonometry Questions

Previous in All Question      Next in All Question      

Previous in Trigonometry      Next in Trigonometry      

Question Number 18588 by Joel577 last updated on 25/Jul/17

$$\sin x=\frac{2a+3}{a+1}$$$$\mathrm{How}\mathrm{many}a\mathrm{that}\mathrm{can}\mathrm{satisfy}\mathrm{the}$$$$\mathrm{equation}\mathrm{above}?$$

Answered by ajfour last updated on 25/Jul/17

$$-1⩽\frac{2\mathrm{a}+3}{\mathrm{a}+1}⩽1;\mathrm{a}\ne -1$$$$\mathrm{CaseI}:\mathrm{if}\mathrm{a}>-1$$$$-\mathrm{a}-1⩽2\mathrm{a}+3\mathrm{and}2\mathrm{a}+3⩽\mathrm{a}+1$$$$\Rightarrow \mathrm{a}⩾-\frac{4}{3}\mathrm{and}\mathrm{a}⩽-2$$$$\mathrm{both}\mathrm{cannot}\mathrm{be}\mathrm{true}\mathrm{simultaneously}$$$$\mathrm{Case}\mathrm{II}:\mathrm{a}<-1$$$$-\mathrm{a}-1⩾2\mathrm{a}+3\mathrm{and}2\mathrm{a}+3⩾\mathrm{a}+1$$$$\Rightarrow \mathrm{a}⩽-\frac{4}{3}\mathrm{and}\mathrm{a}⩾-2$$$$\mathrm{with}\mathrm{a}<-1$$$$\Rightarrow \mathrm{a}\in [-2,-\frac{4}{3}].$$

Commented by Joel577 last updated on 25/Jul/17

$$thankyouverymuch$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com