Find the solutions of \(\displaystyle{\sin{{z}}}={3}\)

Quinn Moses

Quinn Moses

Answered question

2022-04-05

Find the solutions of
sinz=3

Answer & Explanation

gsmckibbenx7ga

gsmckibbenx7ga

Beginner2022-04-06Added 17 answers

you have
sinxcoshy=3, cosxsinhy=0
take the second equation. you have
sinhy=0y=0
cosx=0, x=±π2+2kπ
putting y=0, in the first equation gives sinx=3 which has no real solution. we are now left with
x=±π2+2kπcoshy=±3
since coshy1, we only need to solve
coshy=3e2y6ey+1=0ey=3±23y=ln(3±22)
the solutions are
sin1(3)=±π2+2kπ+iln(3±22)

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