Representation of trigonometric functions using Euler's formula

• http://takeno.iee.niit.ac.jp/~shige/math/lecture/basic3/hyper1/node7.html
  • $\cos x=\frac{e^{ix}+e^{-ix}}{2}\sin x=\frac{e^{ix}-e^{-ix}}{2i}$
• 数式の変換は理解したが、変換後の式の意味を理解したい
  • cos
    • e^ix、x=1, -1以外の場合は複素数だよな
    • 
      • 足すとReだけが残るということか、理解(blu3mo)(blu3mo)
  • じゃあ、気持ちとしてはe^ixが持つ円環性(?)を使ってcos/sinを表現している感じか
• http://takeno.iee.niit.ac.jp/~shige/math/lecture/basic3/hyper1/node7.html
  • $\cos x=\frac{e^{ix}+e^{-ix}}{2}\sin x=\frac{e^{ix}-e^{-ix}}{2i}$
• I understand the transformation of the equations, but I want to understand the meaning of the transformed equations.
  • For cos:
    • When x is not equal to 1 or -1, e^ix is a complex number, right?
    • 
      • So, adding the terms results in only the real part, is that correct? I understand (blu3mo)(blu3mo)
  • So, it seems like we are expressing cos/sin using the circular nature (?) that e^ix possesses.