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## Homework Statement

sorry if the title is not that descriptive

## Homework Equations

i is the imaginary number

e is 2.7...

x is any anlgle in radians that is... um see the example I explain it

sin x = +/- i/2 (1/e^(ix) +/- e^(ix))

I will use a example in atempt at a solution to show you how to use this equation

## The Attempt at a Solution

the first +/- depends on were the angle is located on the unit circle

the second +/- depends on if the angle is smaller or larger than pi/4

- if it is smaller than pi/4 (by the way pi as in 3.14...) just simple enter your angle in the equation above and make the +/- a "-" in its radian measure

- if it is larger than pi/4 take your angle and subtract pi/4 from it and use that as your x and use a "+" instead of minus in the equation

- if anlge is greater than pi/2 use coresponding angle in the first quadrant if you want and just work out the "+/-" in the very begining of the equation

EXAMPLE

I want to know what the sin of 60 degrees is... I know it is SQRT(3)/2 but i'll use the formula above for a demonstration ok...

so 60 degrees in radians is pi/3 which is greater than pi/4 so I have to add pi/4 from pi/3... I'll do this in degrees sense it is easier... 60-45 = 15 degrees

and now what I want to do is take that angle and do 45 minus that angle

45-15 = 30 degrees = pi/6

now just plug this into the equation above

sin x = +/- i/2 (1/e^(ix) +/- e^(ix))

sin x = + i/2 (1/e^((i pi)/6) + e^((i pi)/6) and the calculator gives .8660254038 i

not really sure why it gives the i??? can someone answer that???

if you remove the i this is the exact value for sin pi/3 or simple SQRT(3)/2

try using the equation for other angles for example

sin 1 degree = i/2(1/e^((i pi)/180) - e^((i pi)/180)) = .0174524064 which is the exact value of sin 1 degree

MY QUESTION is how do I go backwards

for example

sin x = +/- i/2 (1/e^(ix) +/- e^(ix)) = SQRT(3)

how do I solve for x???

THANK YOU SO MUCH