Trigonometry - Trigonometric Graphs and Parameters

Trigonometry - Trigonometric Graphs and Parameters

Secondary 4
8 marks
  1. List item image

    The diagram shows the curve \(y = a + 6\cos bx\) for \(0 \le x \le \frac{2\pi}{3}\), where \(a\) and \(b\) are positive constants. The curve meets the \(x\)-axis at the point \(\left(\frac{2\pi}{3}, 0\right)\). The curve has a maximum point at \((0, 9)\) and a minimum point at \(M\).

    Find the value of \(a\) and of \(b\).

    [3]

    1. Sketch, on the axes below, the graphs of \(y = -3\sin x\) and \(y = 1 - \frac{2x}{\pi}\) for \(0 \le x \le 2\pi\).

      [3]
      Sub-item image
    2. Find the number of solution(s) of the equation \(2x = \pi + 3\pi\sin x\) for \(0 \le x \le 2\pi\).[2]
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