March 2020
Intermediate to advanced
608 pages
14h 31m
English
Content preview from Robot Modeling and Control, 2nd Edition
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Appendix ATRIGONOMETRY
A.1 The Two-Argument Arctangent Function
The usual inverse tangent function returns an angle in the range ( − π/2, π/2). In order to express the full range of angles we will find it useful to define the so-called two-argument arctangent function, Atan2(x, y), which is defined for all (x, y) ≠ (0, 0) and equals the unique angle θ ∈ [ − π, π] such that
(A.1)
This function uses the signs of x and y to select the appropriate quadrant for the angle θ. For example, 
, while 
. If both x and y are zero, then Atan2 is undefined.
A.2 Useful Trigonometric Formulas
Below is a list of trigonometric identities that are used to derive various expressions related to forward, inverse, and velocity kinematics.
Pythagorean Identities
Reduction Formulas
Sum-Difference Identities
Double-Angle Identities
Half-Angle Identities
Law of Cosines
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