4.1 Introduction

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Angles degrees and radians

Most computers do calculations in radians

Angle quadrants,

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,