3D trigonometry in Shanghai Download

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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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