Graphing Cotangent Functions

Question

Pre Cal
Graphing Cotangent Functions

y=\frac{1}{4}cot(x- \frac{ \pi }{2})

FIND
-the period
-Four Vertical Asymptotes
- x-intercepts
-intermediate points
- and graph

Answer 1

y = ¼cot(x-pi/2) has the same period as y = cot x but it's shifted to the right by pi/2.

So the period is pi.  Normal vertical asymptotes for y = cot x are based on sin x in denominator (cot x = cos x / sin x) and would have V.A. at 0 and pi etc. but these V.A.s are shifted to x = pi/2 and 3pi/2, etc in this case... Two more V.A.s are

x=-pi/2 and x = -(3/2)pi.

 

x-intercepts(when y = 0) occur when cos (x-pi/2) so that means x = 0 ± any multiple of pi...e.g. 

 

Consult your calculator or textbook or Google graphs of cotangent function for hints on graphing.