a) Solve the following trigonometric equation: A = cosX + AsinX, for some angle X.
b) The imaginary number i is equal to √-1. Use part a) to solve i = cosX + isinX.
You will have used degrees to answer parts a and b. However, the mathematics below requires the use of radians. Convert degrees to radians by multiplying the degree measurement by π/180.
You will now find a value of i^i.
This will require the euler identity e^iX = cosX + isinX, part b) and exponent arithmetic.
c) Evaluate, for one value, i^i.
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So I honestly have no idea how to start this off haha. Could someone help out? Obviously you don't need to solve the whole thing - i just need to know how to start it off. Thanks!
A = cosX + AsinX, for some angle X.
Cos x = A ( 1- sin x )
Cos2x/2 – sin2 x/2 = A ( cos x/2 – sin x/2 )2
[Cos x/2 + sin x/2 ]/ [cos x/2 – sin x/2] = A
[ 1 + tan x/2 ]/[ 1- tan x/2 ] = A
1/[ tan ( π/4+ x/2 ) ] = A
I am sure now you can finish it