maths 2

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
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)


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.

  1. 👍 0
  2. 👎 0
  3. 👁 124
asked by Jake

Respond to this Question

First Name

Your Response

Similar Questions

  1. 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

    asked by Jake on January 14, 2007
  2. 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

    asked by ann on January 20, 2012
  3. math

    Original Question is: how many 1/2 miles are in 12 miles? write the division question 12 divided by 1/2= 24 what multiplication question could the model also answer? 12 x 2 =24 This is the one I didn't understand Write the

    asked by Libby on December 10, 2013
  4. Math

    My original question: How many gallons of paint are necessary to paint the walls of a 15' by 12' room with an 8' ceiling if one gallon of paint covers 80 square feet? Your response is quite clear to me. Please write it in simple

    asked by Garnett on June 13, 2011
  5. English

    1. The following question asks about one or more selections from your Literature textbook. You may use your textbook to answer this question. From the following list, choose two poems for this constructed response: ‟Concrete

    asked by Love WINS on March 20, 2019
  6. Algebra

    How do I express this in algebraic form? And could you please explain how you came up with the expression? "Come up with a number. Add 3 to it. Muliply by 1 more than the original number. Subtract 3. Divide by the original number.

    asked by anonymous on August 24, 2010
  7. math,correction

    Problem #1 subtract. Express your answer in simplest form (3x)/(18) minus (x)/(18) MY steps: (3x-x)/(18) = (2x)/(18) and answer: (2x)/(18) Problem #18 write in simplest form. (3x^5)/(15x^12) My steps: (3)/(15) = .60 x^5-12 = x^-7

    asked by jasort20 on March 18, 2007
  8. Software

    The questions said List four major functions of an OS? The answer i put was Function 1: Provide a user interface Function 2: Manage files Function 3: Manage hardware Function 4: Manage applications Is my answer correct?

    asked by DJ on February 10, 2013
  9. software

    The questions ask List four major functions of an OS. My answer: Function 1: Provide a user interface Function 2: Manage files Function 3: Manage hardware Function 4: Manage applications Is my answer correct?

    asked by DJ on February 12, 2013
  10. Accounting

    Considering how organization must manage cash, receivables, and inventories. Which of the three variables is the most important to manage? In my opinion I would have to say that the cash would be the most important to manage. Am I

    asked by Nick on September 7, 2011

More Similar Questions