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.

Tangent

                                

When you look at the unit circle you realize that tangent in positive in 1st and 3rd quadrant and negative in the 2nd and 4th quadrants, so when you unfold the unit circle in the graph you divide it by quadrants. To mark the quadrants you label them with the radians of the quadrants so it's pi/2, pi, 3pi/2, and 2pi, so since tangent is positive in the 1st & 3rd quadrant they would have asymptotes at pi/2 and 3pi/2.. In the graph the second "quadrant" is negative while the third quadrant is positive, the graph has to stay in between the two asymptotes so the tangent graph will start in the negative and go up to the positive without touching the asymptotes. 

Cotangent

                                 

For cotangent everything is mostly the same but the ration is the inverse of tangent,which makes a huge difference in the graph. The ratio is now x/y which we now have to find where x=0, x is 0 at pi and 2 pi. The asymptotes for cotangent will now lie at pi and two pie which means that they just shifted, when they shifted the signs now start from positive to negative which will make the graph downhill.

Secant 

Secant, just like cosine, is positive in the 1st and 4th quadrants and negative in the 2nd and 3rd quadrants. The asymptotes for this graph will lie on pi/2 and 3pi/2. Therefore that means the in quadrant 1&4 the parabolas will be above the positive cosine but with the inverse direction. Now in quadrants 2&3 will be below the positive cosine and will also have the inverse direction. 

Cosecant 

For cosecant, just like sine, it will be positive in the 1st and 2nd quadrant and negative in the 3rd and 4th quadrant. The asymptotes for cosecant would be on pi and 2pi since you have to find where y=0. That means that in the 1&2 quadrant it will have a parabola at the peak of the amplitudes with an inverse direction. Then in the 3&4 quadrant it will be negative  and heading at an inverse direction of  the amplitude. It would be very similar to the sine graph.