section_path: Identities/Trigonometric identities/Euler's formula
section_name: Euler's formula
paragraph_text: Euler's formula
  
  Euler's formula, which states that e i x = cos x + i sin x {\displaystyle e^{ix}=\cos x+i\sin x}, produces the following analytical identities for sine, cosine, and tangent in terms of e and the imaginary unit i: