Unit T Big Question #3

• Why is a "normal" tangent graph uphill, but a "normal" cotangent graph downhill?

Tangent graph is uphill. When we graph tangent, we actually only graph tangent from Quadrant 2 and 3. There is a part right before the asymptote that has half a line going uphill. That part is actually in Quadrant I because tangent in Quadrant I is positive. So as we move to tangent in Quadrant II, we will draw a line from negative value and going up to positive value. Because tangent in Quadrant II is negative but Quadrant II and Quadrant III connect (w/o being cut by the asymptote), which means the graph for tangent is uphill. However, cotangent graph is downhill because the reciprocal of tangent is cotangent. So the way tangent graph looks will flip and turn into cotangent graph which explains why cotangent graph is downhill whereas tangent graph is uphill.

From math.tutorvista.com
This image shows where tangent graph actually lies which also help to explain why the graph go uphill.


From algebra2c.wikispaces.com
This image is for cotangent graph. It shows why the cotangent graph goes down hill.