Write down the principal value of $\sin^{-1} \left( -\frac{1}{2} \right)$ in radian as a multiple

Question

Write down the principal value of $\sin^{-1} \left( -\frac{1}{2} \right)$ in radian as a multiple of $\pi$.[1] The diagram shows the curve $y = a \sin bx + c$ for $0 \le x \le \pi$ radians. The curve has a maximum point at $\left( \frac{\pi}{4}, 3 \right)$ and a minimum point at $\left( \frac{3\pi}{4}, -7 \right)$. Explain why $c = -2$.[2] Explain why $b = 2$.[2] Hence find the equation of the curve.[2]

Accepted Answer

(a) $-\dfrac\pi6$ (b)(i) $c=-2$ (ii) $b=2$ (iii) $y=5\sin2x-2$

2023 Ahmad Ibrahim Sec AM S3 EOY Q5

2023 Ahmad Ibrahim Sec AM S3 EOY Q5

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