Unit T Big Question #3

Why is a "normal" tangent graph uphill, but a "normal" tangent graph downhill.

This has to do with the Unit Circle, ASTC, and the ratios for tangent and cotangent. The ratio for tangent is sin over cosine while the ratio for cotangent is cosine over sine.For tangent, this means that whenever cosine is zero, there will be an asymptote because it is the denominator. For cotangent, this means that whenever sine is zero, there will be an asymptote because it is the denominator. In the Unit Circle, cosine is zero at 90 degrees (pi/2) and 270 degrees (3pi/2) and sine is zero at 0 degrees (0 radians) and at 180 degrees (pi). This means that there will be asymptotes at pi over 2 and at 3pi over 2 for the tangent graph; 0 and pi for the cotangent graph. ASTC will cause the tangent graph to go uphill and the cotangent graph to go downhill because of where the asymptotes are placed.