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 1, its minimum is -3, and its least positive period is 16 pi radians. Determine a,b,c, then sketch the curve for 0 <= x <= 16 pi, labelling endpoints and turning points.
Solution:
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Answer:\(a=2,\ b=\dfrac{1}{8},\ c=-1\); \(A=2\); \(T=16 \pi\); \(-3\le y\le 1\); \(\text{key points:}\hspace{0.5em}(0,-1),\ (4 \pi,1),\ (8 \pi,-1),\ (12 \pi,-3),\ (16 \pi,-1)\).
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