Saturday

March 28, 2015

March 28, 2015

Posted by **Jake** on Sunday, January 14, 2007 at 3:35pm.

cosacoshb-isinasinhb=4

to

2m(pi)+/- iarccosh4

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)

So,

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**

**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 ...

Maths - For logarithms, if asked to write in simplest form, is it better to ...

chemistry - I dont understand this zwitterion form . Here is the question. write...

Leadership for Organizations - Why is it important for a leader to be able 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 ...

MATHS - Tim spent $1450 on a bicycle and 3/7 of the remainder on a camera. He ...