In the interval 0 </ x < 2pi, determine the equations of all asymptotes for the function y=tan x.

Question

a) x=0
b) x=pi/2
c) x=0, x=pi
d) x=pi/2, 3pi/2

Answer 1

See if you can figure out what the values of tan(x) are at x=0,π/2, π and 3*pi;/2 to get an idea.
Even better, look up the graph of tan(x), noting that tan(-x)=-tan(x) (odd function) and tan(x) = tan(x+π).
See for example:
http://images.google.ca/imgres?imgurl=http://www.analyzemath.com/trigonometry/graph_tangent.gif&imgrefurl=http://www.analyzemath.com/trigonometry/properties.html&usg=__15mZqtEGVbBJpy38TrM4b8suxSM=&h=297&w=338&sz=5&hl=en&start=2&tbnid=0RO3fUwazvjljM:&tbnh=105&tbnw=119&prev=/images%3Fq%3Dtangent%2Bfunction%26gbv%3D2%26hl%3Den%26sa%3DG