Complex Analysis: Theory and Applications · Problem 9.4.7

Applications of Harmonic Functions — Howell & Matthews

Mathematics — Complex Analysis · trigonometric-mapping-exercise

Problem

(a) Find lim⁡y→+∞Arg⁡[sin⁡(π6+iy)]\lim_{y \to +\infty} \operatorname{Arg}[\sin(\frac{\pi}{6} + iy)]. (b) Find lim⁡y→+∞Arg⁡[sin⁡(−2π3+iy)]\lim_{y \to +\infty} \operatorname{Arg}[\sin(-\frac{2\pi}{3} + iy)].

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