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Question Number 93118 by  M±th+et+s last updated on 11/May/20

sin(x)=a  −1≤a≤1

$${sin}\left({x}\right)={a} \\ $$$$−\mathrm{1}\leqslant{a}\leqslant\mathrm{1} \\ $$

Answered by Rio Michael last updated on 11/May/20

sin (x) = a for −1 ≤a ≤ 1  ⇒ x = πn + (−1)^n  sin^(−1) a   where sin^(−1) a is in radians  or x = 180° n +(−1)^n  sin^(−1) a  where sin^(−1) a is in degrees

$$\mathrm{sin}\:\left({x}\right)\:=\:{a}\:\mathrm{for}\:−\mathrm{1}\:\leqslant{a}\:\leqslant\:\mathrm{1} \\ $$$$\Rightarrow\:{x}\:=\:\pi{n}\:+\:\left(−\mathrm{1}\right)^{{n}} \:\mathrm{sin}^{−\mathrm{1}} {a}\: \\ $$$$\mathrm{where}\:\mathrm{sin}^{−\mathrm{1}} {a}\:\mathrm{is}\:\mathrm{in}\:\mathrm{radians} \\ $$$$\mathrm{or}\:{x}\:=\:\mathrm{180}°\:{n}\:+\left(−\mathrm{1}\right)^{{n}} \:\mathrm{sin}^{−\mathrm{1}} {a} \\ $$$$\mathrm{where}\:\mathrm{sin}^{−\mathrm{1}} {a}\:\mathrm{is}\:\mathrm{in}\:\mathrm{degrees} \\ $$

Commented by  M±th+et+s last updated on 11/May/20

thank you sir

$${thank}\:{you}\:{sir}\: \\ $$

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