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我们把相同大前提下彼此之间具有因果关系的一组子题称之为相关题。从形式上看,相关题具有延伸性,往往只有在正确解答出前面题后,才能解出后面题。因此,在数学复习中要注意发挥这类题的作用,以利培养学生的思维能力和综合运用所学知识解决实际问题的能力。例1 设A、B为平面M内两点,PA、PB分别是平面M的垂线和斜线,点A和点B分别是垂足和斜足:在M内过点B引直线BC。使∠ABC=β∠PBC=γ,且pB和平面M成角a。 (1)求证:Cosy=Cosa·COSβ; (2)设COsr=4/3,且Cos(a+β)=1/2,求cos(a-β)的值: (3)如果cosa、 Cosβ是方程4x~2-4x+1=0的根,求点p到平面m的距离与点p到BC的距离的比。
We call a group of sub-topics that have a causal relationship with each other under the same general premise as related questions. In terms of form, the relevant questions have extensibility, and often only after the correct answers to the previous questions can they be solved. Therefore, in the review of mathematics, we must pay attention to the role of such questions in order to facilitate the cultivation of students’ thinking ability and the ability to comprehensively apply the knowledge they have learned to solve practical problems. Example 1 Let A and B be two points in plane M. PA and PB are perpendicular lines and diagonal lines of plane M respectively. Points A and B are foot and oblique foot respectively: in M, the point B is taken as the straight line BC. Let ∠ ABC = β ∠ PBC = γ, and pB and plane M make an angle a. (1) Proof: Cosy=Cosa·COSβ; (2) Let COsr=4/3, and Cos(a+β)=1/2, find the value of cos(a-β): (3) If cosa, Cosβ It is the root of the equation 4x~2-4x+1=0 and the ratio of the distance from the point p to the plane m to the distance from the point p to the BC.