maths 2

posted by .

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
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.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. REPOST!PLZ HELP!ALGEBRA!

    You give up too easily. How? I posted how to get the answer below at the original question. OK but I replied... As did I. Well...I replied...again... Maybe you do understand this for horizontal lines. If you interchange x with y, vertical
  2. Maths

    How do I write arcsin4 in the form a+ib. I know the answer but do not Know how to get to it Take sinus of both sides: 4 = sin(a)cosh(b) + i cos(a)sinh(b) Equate real and imaginary parts. You then see that you can put a = pi/2. And …
  3. algebra

    How do you do this: Write an exponential function of the form y=ab^x that has a graph through (-2, 25) and (1, 10). This is what I have so far: 10=ab^1 10/b=a y=10/b*b^x 2/25=10b^-3 .008=b^-3 Then I am stuck. Am I doing it right so …
  4. Algebra

    The answer in the book however says -(5x^2-17x-9)/(x-3)(x+2) so I don't know what I am doing wrong, can you take me step by step through the problem. I have a lot of problems, but I think once I understand what I am doing wrong with …
  5. arithmetic

    I know that this question had already been answered. But still I could not understand. Calculate this question and write the answer in standard form.The answer should come 5*10. (4.5*10^12)divided by (9*10^10)
  6. chemistry

    I don't understand this zwitterion form . Here is the question. write the zwitterion form of the amino acid cysteins shown in the follwing figure. If the pI for cysteine is 5.1 at what pH will the zwitterions be the predominant form?
  7. Leadership for Organizations

    Why is it important for a leader to be able to manage across cultures?
  8. algebra

    could you please check this answer for me and correct. thanks given equation point slope form linear equation to use to do question. y-3 = 3(x+1) question rewrite this equation in standard form y- 3 + 3 = 3x - 3x +3 + 3 -3x+ y = 6 …
  9. Maths

    For logarithms, if asked to write in simplest form, is it better to write the argument in radical form or exponential form.
  10. math

    Original Question is: how many 1/2 miles are in 12 miles?

More Similar Questions