Is it possible to calculate the value of \delta from

Sarah-Louise Prince

Sarah-Louise Prince

Answered question

2022-02-27

Is it possible to calculate the value of δ from the relation
δ=sin1(5.4i) where i=1?

Answer & Explanation

husudiwareh

husudiwareh

Beginner2022-02-28Added 7 answers

Let δ=x+iy
So, sin(x+iy)=5.4i
Now, sin(x+iy)=sinxcos(iy)+cosxsin(iy)=sinxcoshy+icosxsinhy
Equating the real parts, sinxcoshy=0sinx=0 as coshy1 for real y
So, cosx=±1
If cosx=1,x=2mπ where m is any integer
and sinhy=5.4eyey2=2755(ey)254ey5=0
Solve for ey which is >0 for real y
If cosx=1, x=2(n+1)π where n is any integer
and sinhy=5.4eyey2=2755(ey)2+54ey5
Solve for ey which is >0 for real y

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