Identities for sin x that Came from Medical Imaging
نویسندگان
چکیده
The article describes some interesting and possibly not previously noticed nonlinear differential identities satisfied by exponential and trigonometric functions. Both formulation and the proofs of these relations do not require mathematics knowledge beyond standard differentiation rules and high school algebra. Surprisingly, the research that produced these identities was devoted to medical imaging (computerized tomography). A brief description of the origin of these identities is provided. Relations with some other topics are also briefly mentioned.
منابع مشابه
Notes for the Physics-Based Calculus workshop
1 Trigonometric Functions We recall the following identities for trigonometric functions. Theorem 1.1. For all x ∈ R, cos(−x) = cos(x) and sin(−x) = − sin(x). Theorem 1.2. For all α, β ∈ R, cos(α + β) = cos(α) cos(β)− sin(α) sin(β). Theorem 1.3. For all α, β ∈ R, sin(α+ β) = sin(α) cos(β) + cos(α) sin(β). Proof. For small positive angles (so α+ β is less than a right angle), the identities from...
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ورودعنوان ژورنال:
- The American Mathematical Monthly
دوره 120 شماره
صفحات -
تاریخ انتشار 2013