The diagram shows part of the graph of $y = a \tan bx + c$. The graph has vertical asymptotes at \

Question

The diagram shows part of the graph of $y = a \tan bx + c$. The graph has vertical asymptotes at $x = -4\pi$ and $x = 4\pi$ and passes through the points $P$ and $Q$. Explain why $b = \frac{1}{8}$.[2] Hence find the equation of the curve.[2] The function $\mathrm{f}(x)$ is defined by $\mathrm{f}(x) = 4 + 3 \sin 2x$ for $0^\circ \le x \le 360^\circ$. Sketch the graph of $y = \mathrm{f}(x)$ on the axes below.[2]

Accepted Answer

(a)(i) $b=\frac18$ (shown). (ii) $y=4\tan\left(\frac x8\right)+3$. (b) Two cycles, midline $y=4$, maxima $(45^\circ,7),(225^\circ,7)$, minima $(135^\circ,1),(315^\circ,1)$.

2024 FMSS PRELIMS P1 Q4

2024 FMSS PRELIMS P1 Q4

Solution:

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