Question Number 93118 by M±th+et+s last updated on 11/May/20
$${sin}\left({x}\right)={a} \\ $$$$−\mathrm{1}\leqslant{a}\leqslant\mathrm{1} \\ $$
Answered by Rio Michael last updated on 11/May/20
$$\mathrm{sin}\:\left({x}\right)\:=\:{a}\:\mathrm{for}\:−\mathrm{1}\:\leqslant{a}\:\leqslant\:\mathrm{1} \\ $$$$\Rightarrow\:{x}\:=\:\pi{n}\:+\:\left(−\mathrm{1}\right)^{{n}} \:\mathrm{sin}^{−\mathrm{1}} {a}\: \\ $$$$\mathrm{where}\:\mathrm{sin}^{−\mathrm{1}} {a}\:\mathrm{is}\:\mathrm{in}\:\mathrm{radians} \\ $$$$\mathrm{or}\:{x}\:=\:\mathrm{180}°\:{n}\:+\left(−\mathrm{1}\right)^{{n}} \:\mathrm{sin}^{−\mathrm{1}} {a} \\ $$$$\mathrm{where}\:\mathrm{sin}^{−\mathrm{1}} {a}\:\mathrm{is}\:\mathrm{in}\:\mathrm{degrees} \\ $$
Commented by M±th+et+s last updated on 11/May/20
$${thank}\:{you}\:{sir}\: \\ $$