Sketching a sine curve and its reciprocal cosecant graph with asymptotes and a turning point

Sketching a sine curve and its reciprocal cosecant graph with asymptotes and a turning point

IB Year 6 | Grade 12
6 marks
  1. Sketch the graph of \(y=\sin2x\) for \(0\le x\le\pi\).[2]
  2. On a separate set of axes, sketch the graph of \(y=3\operatorname{cosec}2x\) for \(0<x<\pi\). State the coordinates of its local maximum point and the equations of all its vertical asymptotes.[4]

Solution:

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Answer:(b) local maximum \(\left(\frac{3\pi}4,-3\right)\), asymptotes \(x=0,\ x=\frac\pi2,\ x=\pi\)

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