Transcript

PANDA – Cycle 2 Basic Trigonometry 3D trigonometry in Shanghai The topic, 3D trigonometry, is introduced at Session 3 and Session 4, Chapter 14 line and plane in 3D, at the beginning of Y13. The whole chapter has four sessions as following: 1. Planes and Their Basic Properties A, B present point. present plane. presents straight line. Axiom 1: ∈ , ∈ , ∈ , ∈ , then Axiom 2: Two different planes , if ∈ ∩ , then ∩ = , ∈ 2. Relationship between Two Lines in Space extended from 2D. If two sides of the angle are parallel to anther angel's two sides, then these two angles either are the same size or add up to 180. The definition of skew lines PANDA – Cycle 2 Basic Trigonometry Example 3: A cube − ′′′′, the length is . Find the size of angle by skew lines. (1) ′′; (2) ′ ′; (3) ′ ′. 3. Relationship between Line and Plane in Space Part A: the distance The distance between Point A and Plane (1), the distance between line and Plane (2), the distance between Plane and Plane (3): PANDA – Cycle 2 Basic Trigonometry Example A cuboid − ′′′′, the lengths of ′ , are 3cm, 4cm and 5cm respectively. Find (1) the distance between point A and point C'; (2) the distance between point A and length B'C'; (3) the distance between length AB and plane A'B'C'D'; (4) the distance between skew lines AD and A'B'. Part B the angle The angle between line and plane Example A cube − ′′′′, the length is . Find the size of angle by line and plane. (1) ′ ′′′′; (2) ′ ′′′′ PANDA – Cycle 2 Basic Trigonometry 4. Relationship between two Planes The definition of dihedral angle, − − Example There is a cube − ′′′′, find the size of dihedral angle − ′′ − ′

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