Section+5.3

=Section 5.3= I. The Tangent Function - A **vertical asymptote** is a vertical (dashed) line that represents a value of x for which the function is not defined.

II. The Cotangent Function - The cotangent function is similar to the tangent function in that it is a quotient involving the sine and cosine functions. - cotx= cosx / sinx - X-Intercepts are at multiples of pi/2
 * The tangent functions and cotangent functions have period pi, whereas the secant and cosecant functions have period 2pi.***


 * To graph the tangent and cotangent functions, first identify the vertical asymptotes and x-intercepts, and then find values of the function within a period (i.e., between the asymptotes).***


 * To find the graphs of secant and cosecant functions, first graph their guide functions (cosine and sine respectively), and then label vertical asymptotes that correspond to x-intercepts of the guide function.***


 * The graphs of the secant and cosecant functions resemble the letter U opening up or down.***


 * The secant and cosecant functions are positive when their guide function is positive and negative when their guide function is negative.***