A tangent curve from asymptotes and points
A tangent curve from asymptotes and points
6 marks
TGM Original
A curve has equation y=atan(bx)+c, where a,b>0 and x is measured in radians. Two consecutive vertical asymptotes are x=3pi and x=9pi. The y-intercept is (0,-1) and the curve passes through (3pi/2,1). Find a,b,c, then sketch the curve for 0 <= x 6pi, labelling all asymptotes and finite endpoints.
Solution:
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Answer:\(a=2,\ b=\dfrac{1}{6},\ c=-1\); \(T=6 \pi\); \(\text{asymptotes:}\hspace{0.5em}x=3 \pi\); \(\text{no amplitude}\).
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