Monday, April 21, 2014

BQ#4 – Unit T Concept 3 Why is a “normal” tangent graph uphill, but a “normal” cotangent graph downhill?


             

Tangent: Tangent go up because the asymptotes of tangent are found wherever x=0 (tan=y/x) and that is in pi/2 and 3pi/2. Since you can't touch the asymptotes, the only to go through the pattern correctly is to go up in the 1st quadrant since it is positive. (if it were to go down then it would have to go through the asymptote). In quadrants 2-3 they would from positive to negative so the whole period fits in between the asymptotes Pi/2 and 3pi/2. The fourth quadrant is negative so it comes from underneath the 0.
Cotangent: Cotangent goes downward because the asymptotes are found at 0, pi, 2pi. the 1st-2nd quadrants are positive and negative so they can complete a complete period in between the asymptotes 0 and pi.  Same thing applies for in between pi and 2pi with 3rd being positive and 4th being negative.  

***REMINDER*** These are just snapshots, the whole graphs are infinite.

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