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 4, its minimum is -2, and its least positive period is 2160 degrees. Determine a,b,c, then sketch the curve for 0 <= x <= 2160, labelling endpoints and turning points.
Solution:
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Answer:\(a=3,\ b=\dfrac{1}{6},\ c=1\); \(A=3\); \(T=2160^\circ\); \(-2\le y\le 4\); \(\text{key points:}\hspace{0.5em}(0,4),\ (540,1),\ (1080,-2),\ (1620,1),\ (2160,4)\).
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