Complex Number Trigonometry You can represent the trigonometric functions as complex numbers cosθ=eiθ+e−iθ2\cos\theta = \frac{e^{i\theta} + e^{-i\theta}}{2}cosθ=2eiθ+e−iθ sinθ=eiθ−e−iθ2i\sin\theta = \frac{e^{i\theta} - e^{-i\theta}}{2i}sinθ=2ieiθ−e−iθ tanθ=sinθcosθ=1i⋅eiθ−e−iθeiθ+e−iθ=−i⋅eiθ−e−iθeiθ+e−iθ\tan\theta = \frac{\sin\theta}{\cos\theta} = \frac{1}{i}\cdot\frac{e^{i\theta} - e^{-i\theta}}{e^{i\theta} + e^{-i\theta}} = -i\cdot\frac{e^{i\theta} - e^{-i\theta}}{e^{i\theta} + e^{-i\theta}}tanθ=cosθsinθ=i1⋅eiθ+e−iθeiθ−e−iθ=−i⋅eiθ+e−iθeiθ−e−iθQubit