Question Number 194327 by pete last updated on 03/Jul/23
$$\mathrm{If}\:\mathrm{ta4}\theta\:=\:\mathrm{1},\:\mathrm{find}\:\mathrm{the}\:\mathrm{values}\:\mathrm{of}\:\theta. \\ $$
Answered by MikeH last updated on 03/Jul/23
$$\mathrm{tan}\:\mathrm{4}\theta\:=\:\mathrm{1}\: \\ $$$$\Rightarrow\:\mathrm{4}\theta\:=\:\pi{n}\:+\:\frac{\mathrm{1}}{\mathrm{4}}\pi \\ $$$$\Rightarrow\:\theta\:=\:\frac{\mathrm{1}}{\mathrm{4}}\pi{n}\:+\:\frac{\mathrm{1}}{\mathrm{16}}\pi \\ $$$$\theta\:=\:\left\{\frac{\mathrm{1}}{\mathrm{16}}\pi,\:\frac{\mathrm{5}}{\mathrm{16}}\pi,\:\frac{\mathrm{9}}{\mathrm{16}}\pi,…\right\} \\ $$
Commented by pete last updated on 04/Jul/23
$$\mathrm{thank}\:\mathrm{you}\:\mathrm{sir} \\ $$