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4.1 Introduction

• Angles degrees and radians

• Most computers do calculations in radians

• Angle quadrants,

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4.1.1 Functions

• The basic trigonometry functions are,

• Graphs of these functions are given below,

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4.1.2 Inverse Functions

• Inverse Functions

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

• Scilab example,

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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°.

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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,

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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,

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4.1.6 Special Relationships

• The Small Angle Approximation

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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,