4.1.1 Functions

 

• The basic trigonometry functions are,

 

• Graphs of these functions are given below,

 

 

 

 

 

 

 

 

 

 

 

 

4.1.2 Inverse Functions

 

• Inverse Functions

 

 

• Note: trig calculations can take a while and should be minimized or avoided in programs.

 

• Scilab example,

 

4.1.3 Triangles

 

 

• 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°.

 

 

 

 

4.1.4 Relationships

 

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

 

 

• Scilab for trig identities,

 

• These can also be related to complex exponents,

 

 

 

4.1.5 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,

 

 

4.1.6 Special Relationships

 

• The Small Angle Approximation

 

4.1.7 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,