5.7. Graphs of Other Trigonometric Functions http://www.ck12.org
Notice wherever cosine is zero, secant has a vertical asymptote and where cosx=1 then secx=1 as well. These
two logical pieces allow you to graph any secant function of the form:
f(x) =±a·sec(b(x+c))+d
The method is to graph it as you would a cosine and then insert asymptotes and the secant curves so they touch the
cosine curve at its maximum and minimum values. This technique is identical to graphing cosecant graphs. Simply
use the sine graph to find the location and asymptotes.
The tangent and cotangent graphs are more difficult because they are a ratio of the sine and cosine functions.
- tanx=cossinxx
- cotx=cossinxx
The way to think through the graph off(x) =tanxis to first determine its asymptotes. The asymptotes occur
when the denominator, cosine, is zero. This happens at±π 2 ,±^32 π...The next thing to plot is the zeros which occur
when the numerator, sine, is zero. This happens at 0,±π,±, 2 π...From the unit circle and basic right triangle
trigonometry, you already know some values of tanx:
- tanπ 4 = 1
- tan(−π 4 )=− 1
By plotting all this information, you get a very good sense as to what the graph of tangent looks like and you can fill
in the rest.