## 1.3 SPATIAL RELATIONSHIPS

### 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, ### 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, #### 1.3.2.1 - Practice Problems

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