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1.3 SPATIAL RELATIONSHIPS

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1.3.1 Trigonometry

• The basic trigonometry functions are,

• Graphs of these functions are given below,

• NOTE: Keep in mind when finding these trig values, that any value that does not lie in the right hand quadrants of cartesian space, may need additions of ±90° or ±180°.

• Now a group of trigonometric relationships will be given. These are often best used when attempting to manipulate equations.

• These can also be related to complex exponents,

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1.3.2 Hyperbolic Functions

• The basic definitions are given below,

• some of the basic relationships are,

• Some of the more advanced relationships are,

• Some of the relationships between the hyperbolic, and normal trigonometry functions are,

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1.3.2.1 - Practice Problems

3. Find all of the missing side lengths and corner angles on the two triangles below,

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1.3.3 Geometry

****************** ADD IN MASS MOMENTS AND DESCRIPTIONS ************

• A set of the basic 2D and 3D geometric primitives are given, and the notation used is described below,

• A general class of geometries are conics. This for is shown below, and can be used to represent many of the simple shapes represented by a polynomial.

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1.3.4 Planes, Lines, etc.

• The most fundamental mathematical geometry is a line. The basic relationships are given below,

• If we assume a line is between two points in space, and that at one end we have a local reference frame, there are some basic relationships that can be derived.

• The relationships for a plane are,