Essays on Tangent

1. An investor does not need to make a decision which portfolio to choose when a risk free asset is included. There is now only one tangent portfolio he can choose. Explain this statement with graphs analysis. The line of possible portfolio risk and return combinations given the risk-free rate and the risk and return of the portfolio of risky assets is called capital allocation line(CAL). For an individual investors and under the assumption of CAPM model that each investor faces homogeneous expectations, the best capital allocation line is the one that offers the highest expected utility in ...

1. The Sine and Cosine graphs are 'complementary', which means that the expression sin2 x + cos2 x = 1 is realized. Therefore, when sin (x) = 1, in that point cos(x) = 0, and vice versa. The same situation is observed when the functions take -1 and 0 values. Therefore, if Sine and Cosine are plotted on the same graphs, they look the same, but as if Cosine function is shifted by pi/2 comparing to Sine. Since Tangent function is obtained as sin x / cos x, then the point x = it should not reach the x-points pi/2, 3pi/2, etc. The ...

Space rendezvous is a precise orbital maneuver, which requires two spacecrafts to arrive at the same orbit, and move at the same speed. Since the orbital velocity is usually not less than 7 km/s, a 1-second error will case a distance of 7 kilometers between the spacecrafts. Such an error is unacceptable, as rendezvous is a prerequisite of docking, which requires spacecrafts to rendezvous as close as some dozen meters. Initially, astronauts were not aware of principles of the space mechanics. Engineer André Meyer says that “to catch something on the ground, one simply moves as quickly as possible ...