Question Number 209763 by Ismoiljon_008 last updated on 20/Jul/24
Commented by Ismoiljon_008 last updated on 20/Jul/24
![Find the number of roots of the following equation in the interval [ −2π;2π ] help please](Q209764.png)
$$\:\:\:\mathscr{F}{ind}\:{the}\:{number}\:{of}\:{roots}\:{of}\:{the}\:{following} \\ $$$$\:\:\:{equation}\:{in}\:{the}\:{interval}\:\left[\:−\mathrm{2}\pi;\mathrm{2}\pi\:\right] \\ $$$$\:\:\:{help}\:{please} \\ $$
Answered by mr W last updated on 20/Jul/24
![4 sin 2x=(√3)+tan x we see there are three roots in [−(π/2),(π/2)] so there are 12 roots in [−2π,2π]](Q209770.png)
$$\mathrm{4}\:\mathrm{sin}\:\mathrm{2}{x}=\sqrt{\mathrm{3}}+\mathrm{tan}\:{x} \\ $$$${we}\:{see}\:{there}\:{are}\:{three}\:{roots}\:{in} \\ $$$$\left[−\frac{\pi}{\mathrm{2}},\frac{\pi}{\mathrm{2}}\right] \\ $$$${so}\:{there}\:{are}\:\mathrm{12}\:{roots}\:{in}\:\left[−\mathrm{2}\pi,\mathrm{2}\pi\right] \\ $$
Commented by mr W last updated on 20/Jul/24
Commented by Ismoiljon_008 last updated on 21/Jul/24
$$\:\:\:{thank}\:{you} \\ $$