A curve has equation y=atan(bx)+c, where a,b0 and x is measured in degrees. Two consecutive vertica

Question

A curve has equation y=atan(bx)+c, where a,b>0 and x is measured in degrees. Two consecutive vertical asymptotes are x=-720 and x=720. The y-intercept is (0,2) and the curve passes through (360,5). Find a,b,c, then sketch the curve for -720 <= x 720, labelling all asymptotes and finite endpoints.

Accepted Answer

$a=3,\ b=\dfrac{1}{8},\ c=2$; $T=1440^\circ$; $\text{asymptotes: }x=-720^\circ,\ x=720^\circ$; $\text{no amplitude}$.

A tangent curve from asymptotes and points

A tangent curve from asymptotes and points

Solution:

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