BQ#3 – Unit T Concepts 1-3

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

a) Tangent

Tangent is related to sine and cosine because the ratio for tangent is sin over cos. Tan and sin and cos have a relationship where if sin or cos is negative then so will be tan. You can reference my BQ 4 for more information here. In quadrant 1 all of the trig functions are positive. In the 2nd quadrant only sine and cosecant are positive but since cosine is negative, so will tangent. This continues to the rest of the quadrants, so basically to make it simpler, if either sine or cosine are negative then so will tangent.

b) Cotangent  

Sine and Cosine relate to Cotangent basically in the same way that tan does. The ratio for cotangent is cos over sin which then basically means that in order to have asymptotes sin has to equal zero. Sine equals zero at 0 or 2pi. From then on the asymptotes repeat forever and the graph will never be able to cross them. 



c) Secant

Secant can be related back to sine and cosine. The ratio for sec is 1 over cos so what that implies is that cos has to equal zero. Cosine can equal zero when it is at 90 degrees or 270 degrees. If that were to be that case, there would be asymptotes. The secant and cosine relate  because the reciprocal of secant is 1 over cosine which also leads to having cosine equal zero. In a cosine graph, the numbers -1 and 1 show up and if you take a look at the graph, -1 and 1 also show up.


d) Cosecant

  The graph above demonstrates a co-secant possibly relate to sine? Well if you remember something sine you know that it is positive in quadrant 1 and 2. The reciprocal ratio for co-secant is 1 over sine. Something that they have in common is that co-secant touches the mountain tops and the valleys of a sine graph.