Unit T Big Question #2

How do the graphs of sine and cosine relate to each of the others? Emphasize asymptotes in your response. 

     a.Tangent? When cosine is zero, it makes tangent become undefined. It will have an asymptote on the points where cos = 0: pi/2 or 3pi/2.  

     b. Cotangent? 

    

Cot is the inverse of tan because tan is sin/cos. Cot is cos/sin. When sin is 0, there is an asymptote because the whole thing is made undefined at that particular part. Tan asymptotes are at pi/2 and 3pi/2 so, to contrast, this means that cot asymptotes are at 0 and pi. Using the graphs, the asymptotes of the graph y = tanx are the x intercepts of the graph of y = cotx. There are vertical asymptotes at each end of the cycle. The asymptote that occurs at pi repeats every pi units.

      

c. secant?

sec is the inverse of cos which means that it is 1/cos and when cosine is 0 in this case, sec becomes undefined as a whole since it is the reciprocal of cosine. When we have undefined as our answer there is going to be an asymptote. These are vertical asymptotes.  The asymptote that occurs at pi/2 repeats every  pi units. The brown lines are the sec graph. The pink line is part of the parent graph of cos.

d. cosecant?

csc is the reciprocal of sin making csc 1/sin. So, when sin is zero in this case, cos becomes undefined anytime sin is 0, thus resulting in an asymptote. The x intercepts of y = sin x are the asymptotes for y = csc x. There are vertical asymptotes. The asymptote that occurs at pi repeats every pi units  

the red is the csc graph and the blue is the parent graph of sin. 

  

    http://www.regentsprep.org/Regents/math/algtrig/ATT7/othergraphs.html