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This chapter examines trigonometry. It starts with a discussion of angles and circular measure. An angle is a measure of rotation or turn, and it is usually specified in degrees. The chapter notes that, despite our familiarity with degrees, a circular measure that is often more useful in a mathematical context is a radian.
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Our purpose here is to establish that a general operator trigonometry created by us 30 years ago provides a natural geometry and useful tool for certain situations occurring in quantum probability. In particular we will embed the Bell–Wigner–Accardi theory of quantum spin systems into this operator trigonometry. We will also establish a new connection
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