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?

-Sine and cosine relate to cosine because of their signs on the unit cicrle. The ratio for tangent is tan(x)=Sin(x0/cos(x). So since the tangent ratio includes sine and cosine, their signs affect the tangent graph. So if sine is postive and cosine is negative, then the tangent group will be negative and go downhill. If sine and cosine is postive then tangent will be postive and going uphill.

b. Cotangent?

-Cotangent is just the reciporcal of tangent. Cotangent's ratio is cot(x)=cos(x)/sin(x). So cosine and sine's signs depend on what way the graph is going. So if sin is negative and cosine is postive then the graph will go downhill because it will make cotangent negative. We get these signs from the unit circle.  Plus it has diffferent asymptotes than tangent. 

c. Secant? 

-For secant, sine does not affect this graph at all. The only one that affects it is cosine. Cosine affects this graph because the ratio for secant is sec(x)=1/cos(x). So this means that cosine determine where the asymptotes go because cosine can equal 0. If cosine is 0 then it is undefined which means there are asymptotes. So cosine affectets secant because of the asymptotes.

d. Cosecant?

                            

                                     

-For cosecant, cosine does not affect this graph at all. The only one that affects it is sine. Sine affects this graph because the ratio for cosecant is csc(x)=1/sin(x). So this means that sine determines where the asymptotes go because sine can equal 0. If sine is 0 then it is undefined which means there are asymptotes. So sine affects cosecant because of the asymptotes.