Beta angle result of the beta angle of the space station at those times. When the orbiter was in-flight (not docked to ISS) and it flew to a beta angle greater than 60 degrees, the orbiter went into "rotisserie" mode, and slowly rotated around its X-axis (nose to tail axis). For flights to ISS, the shuttle could launch during an ISS beta cutout if the ISS would be at a beta less than 60 degrees at dock, and throughout the docked phase. Therefore, the mission duration affected launch timing when the beta cutout dates were approaching. Beta angle The beta angle (formula_1)
Integer triangle cosine equals 0, ±1/2, or ±1. The only ones of these giving an angle strictly between 0° and 180° are the cosine value 1/2 with the angle 60°, the cosine value –1/2 with the angle 120°, and the cosine value 0 with the angle 90°. The only combination of three of these, allowing multiple use of any of them and summing to 180°, is three 60° angles. Conditions are known in terms of elliptic curves for an integer triangle to have an integer ratio "N" of the circumradius to the inradius. The smallest case, that of the equilateral triangle, has