The diagram shows part of the graph of $y = a \sin bx$, where $b 0$, for \(-360^\

Question

The diagram shows part of the graph of $y = a \sin bx$, where $b > 0$, for $-360^\circ \le x \le 360^\circ$. Find the amplitude, the period and the range of values of $y$ corresponding to the interval. Hence find the values of $a$ and $b$. Write down the coordinates of the maximum point(s) and the minimum point(s) of the graph in the given interval.

Accepted Answer

(i) amplitude $\dfrac{5}{2}$, period $360^\circ$, range $-\dfrac{5}{2} \le y \le \dfrac{5}{2}, a = \dfrac{5}{2}, b = 1$; (ii) maxima $\left(-270^\circ, \dfrac{5}{2}\right), \left(90^\circ, \dfrac{5}{2}\right)$; minima $\left(-90^\circ, -\dfrac{5}{2}\right), \left(270^\circ, -\dfrac{5}{2}\right)$

Trigonometry - Trigonometric Graphs and Parameters

Trigonometry - Trigonometric Graphs and Parameters

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