A normal tangent is uphill and a normal cotangent is downhill because of the placement of the asymptotes. For tan it goes uphill because we have asymptotes where cos equals zero(since tan's trig identity is sin/cos and we need to have zero in the denominator to get undefined=asymptotes) and remembering that we need to be in between the asymptotes but not touch them and tan needing to be positive in the first quadrant (because the sin and cos graphs being positive in quadrant one and a positive divided by a positive is positive=tan ) and tan needing to be negative in quadrant two, uphill is the only way you can fit the graph in between the asymptotes. For cot it goes downhill because we have asymptotes when sin equals zero(cot=cos/sin). Cot needs to be positive in the first quadrant(sin and cos are both positive) and negative in quadrant two(sin is postive and cos is negative; positive divided by a negative=negative) and downhill is the only way we can fit the graph in between the asymptotes and it be positive and negative in the second quadrant. To bring it all together the placement of the asymptotes makes a normal tangent uphill and a cotangent downhill.
No comments:
Post a Comment