BQ#4- Unit T- Concept 3

Why is a "normal" Tangent uphill, but a "normal" Cotangent graph downhill? Use unit circle ratios to explain.
According to the unit circle, tangent is positive in the first and third quadrants which is why on the graph, tangent is above the x axis which is positive from 0 to pi/2 and pi to 3pi/2. Also because the asymptotes for tangent are pi/2 and 3pi/2, that explains why tangent is going towards the asymptotes meaning that because tangent stops being positive at the end of the first quadrant it goes toward the asymptote to finish the cycle and then starts going negative to start the second quadrant and so on. That is why a normal tangent graph is uphill at one period.

http://www.mathsisfun.com/algebra/images/tangent-graph.gif

According to the unit circle, cotangent is positive in the first and third quadrants just like tangent that is why on the graph, cotangent is also above the x axis (positive) from 0 to pi/2 and pi to 3pi/2. Also, because the asymptotes for cotangent are 0 and pi, that explains why cotangent is going towards those asymptotes, which means that cotangent stops being positive at the end of the first quadrant going towards the asymptote to finish the cycle and then starts going negative to start the second quadrant and so on. Another reason why it is downhill is also because it is the inverse of tangent so the direction is almost like a mirror image going in a different direction since they are reciprocals of each other since they have different asymptotes it changes the pattern of the graph which makes it go downhill this time instead of uphill. That is why Cotangent is going downhill.


https://algebra2c.wikispaces.com/file/view/Cotangent(X).png/34612489/Cotangent(X).png


                                    WORKS CITED PAGE

TANGENT
COTANGENT