What is the sine of i (initial value prob)

In summary, the conversation is about determining the sine or cosine of i and whether it makes sense to ask for the sine of √(-1) in the context of a second order differential equation. The person is also asking for help with rearranging and determining ω, which they believe ended up being i.
  • #1
fufufu
17
0
what is the sine of "i" (initial value prob)

Homework Statement


What is the sine or cosine of i?
does it make sense to ask what sine of root (-1) is?

im asking because its from 2nd order DE: t^2y'' - ty' + y = 0...y(1) = 1 y'(1) = 1


when i rearrranged and determined omega it ended up being i.. is that wrong??

(omega squared = -(1/t) so omega = i)

?

please help...thanks



Homework Equations





The Attempt at a Solution


 
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  • #2
sinx = (eix - e-ix)/2

so sini = … ?
 
  • #3


fufufu said:

Homework Statement


What is the sine or cosine of i?
does it make sense to ask what sine of root (-1) is?

im asking because its from 2nd order DE: t^2y'' - ty' + y = 0...y(1) = 1 y'(1) = 1


when i rearrranged and determined omega it ended up being i.. is that wrong??

(omega squared = -(1/t) so omega = i)

You didn't show any work and I don't know what ω is that you are talking about nor what the sine or cosine functions have to do with this problem, let alone the sine of i.
 

FAQ: What is the sine of i (initial value prob)

What is the sine of i?

The sine of i is a mathematical concept that refers to the value of the sine function when the input is the imaginary number i. It is expressed as sin(i) and has a value of approximately 0.84147098.

How is the sine of i calculated?

The sine of i is calculated using the Taylor series expansion of the sine function, which can be written as sin(i) = i - (i^3/3!) + (i^5/5!) - (i^7/7!) + ...

What is the significance of the sine of i in mathematics?

The sine of i is important in mathematics because it helps in understanding the behavior of complex numbers and trigonometric functions. It also has applications in fields such as physics, engineering, and signal processing.

Can the sine of i be represented graphically?

Yes, the sine of i can be represented on a complex plane, where the horizontal axis represents the real part and the vertical axis represents the imaginary part. It is a point on the imaginary axis with a value of approximately 0.84147098.

Does the sine of i have any real-world applications?

While the sine of i may not have direct real-world applications, it is a fundamental concept in mathematics and is used in various mathematical and scientific calculations. For example, it is used in the Euler's formula and the Fourier series, which have practical applications in various fields.

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