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2011-W_Wood-Squigonometry

Author(s): W Wood

NA

Keywords: Trigonometric Functions circle squigonometry inverse function trigonmetry

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Abstract

Resource Image The differential equations used to define a unit circle, namely x’(t) = - y(t), y’(t) = (t), x(0) = 1, y(0) = 0 are generalized to produce interesting functions which satisfy trig like identities.

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Wood, W. 2011. Squigonometry. Mathematics Magazine.  84(4): 257-265.

See https://www.tandfonline.com/doi/abs/10.4169/math.mag.84.4.257 . Accessed 29 March 2023.

The differential equations used to define a unit circle, namely

          x’(t) = - y(t),     y’(t) = (t),      x(0) = 1,     y(0) = 0

are generalized to produce interesting functions which satisfy trig like identities. Inverse functions are also studied.  Challenge problems are offered and the imagination can render other such equations for other such shapes.

Keywords: differential equations, parametric equations, circle, trigonometry, trigonometric functions, sine, cosine, squigonometry, inverse function

 

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Author(s): W Wood

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