Posted by Jake on Sunday, January 14, 2007 at 3:35pm.
The original question I had was write arcsin4 in the form a+ib. I manage and understand how to get so far BUT How do I get from
arcsin4 = a + b i --->
4 = sin(a + bi)
sin(a + bi) =
sin(a)cos(bi) + cos(a) sin(bi)
cos(bi) = cosh(b)
sin(bi) = i sin(b)
4 = sin(a)cosh(b) + i cos(a) sinh(b)
The imaginary part of the left hand side is zero, so we must have:
cos(a) sinh(b) = 0
We already know that b can't be zero, because we know that arcsin(4) is not real. This means that a must be plus or minus pi/2.
Equatiiong the real parts gives you:
4 = sin(a)cosh(b)
cosh(b) is positive, it thuis follws that sin(a) must be positive and we must thus choose a = pi/2. And we obtain:
b = plus or minus arccosh(4)
It turns out that the correct analytical continuation of the arcsin function defined for real argument yields the minus sign for b here.
Answer This Question
More Related Questions
- Maths - How do I write arcsin4 in the form a+ib. I know the answer but do not ...
- arithmetic - I know that this question had already been answered. But still I ...
- math - Original Question is: how many 1/2 miles are in 12 miles? write the ...
- chemistry - I don't understand this zwitterion form . Here is the question. ...
- Leadership for Organizations - Why is it important for a leader to be able to ...
- Maths - For logarithms, if asked to write in simplest form, is it better to ...
- REPOST!PLZ HELP!ALGEBRA! - You give up too easily. How? I posted how to get the ...
- Algebra - The answer in the book however says -(5x^2-17x-9)/(x-3)(x+2) so I don'...
- algebra - could you please check this answer for me and correct. thanks given ...
- algebra - How do you do this: Write an exponential function of the form y=ab^x ...