A reconstructed cosine curve
A reconstructed cosine curve
6 marks
TGM Original
A curve has equation y=acos(bx)+c, where a,b>0. Its maximum is -1, its minimum is -5, and its least positive period is 16 pi radians. Determine a,b,c, then sketch the curve for - 8 pi <= x <= 8 pi, labelling endpoints and turning points.
Solution:
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Answer:\(a=2,\ b=\dfrac{1}{8},\ c=-3\); \(A=2\); \(T=16 \pi\); \(-5\le y\le -1\); \(\text{key points:}\hspace{0.5em}(- 8 \pi,-5),\ (- 4 \pi,-3),\ (0,-1),\ (4 \pi,-3),\ (8 \pi,-5)\).
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