BQ#4 – Unit T Concept 3

Why is a “normal” tangent graph uphill, but a “normal” cotangent graph downhill? Use unit circle ratios to explain.

The normal tangent graph is up hill because its ratio consists of (sin/cos): y/x. That meaning that when x is equal to zero the ratio is made undefined. By referring back to the unit circle we can see that x equals zero at pi/2 and 3pi/2, meaning that that is were our asymptotes lye for tangent. Meaning that the graph has to be within those two boundaries. Another thing to keep in mind is that tangent consists of a pattern of positive, negative, positive, negative, depending on what quadrants the graph lys in tells u whether it is up sloping or down sloping. As seen in the image below normal tangent graph is uphill because of where it's boundaries were.

When taking a look at cotangent we first see what ratio it has which is the complete opposite to that of tangent: cos/ sin, x/y. with that we can now refer back to our unit circle and see where y/sin equals zero, because that is where our assymptotes will be. Sine is zero at zero and pi, as you can tell our boundaries are now different, making us fall into different quadrant. Because of that changing the complete look of the graph, making it into a  down sloping graph. Although some part did remain the same which was the pattern of positive, negative, positive,negative.