A reconstructed sine curve
A reconstructed sine curve
6 marks
TGM Original
A curve has equation y=asin(bx)+c, where a,b>0. Its maximum is 5, its minimum is -1, 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:\(a=3,\ b=\dfrac{1}{6},\ c=2\); \(A=3\); \(T=2160^\circ\); \(-1\le y\le 5\); \(\text{key points:}\hspace{0.5em}(0,2),\ (540,5),\ (1080,2),\ (1620,-1),\ (2160,2)\).
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