TRIGONOMETRY: ONTARIO CURRICULUM versus HISTORICAL DEVELOPMENT Carol Miron
Slide 2TRIGONOMETRY IN ONTARIO CURRICULUM Grade 10 (Academic) Find lengths and edges of triangles Trigonometry as proportion of sides Sine and Cosine Law Grade 11 (M/U) Review of triangle trigonometry Transformations of sine & cosine capacities
Slide 3WHY? Crevice from review 10 to review 11 in secondary school arithmetic Examine advancement of these parts of trigonometry in history and how they identify with understudy learning
Slide 4ARISTOTELIAN TRIGONOMETRY: Static Applications Trigonometry used to discover points and lengths/separations statures of structures, trees (comparable triangles)
Slide 5ARISTOTELIAN TRIGONOMETRY: Static Applications Trigonometry used to discover edges and lengths/separations route by stars separations to removed articles (parallax)
Slide 6ARISTOTELIAN TRIGONOMETRY: Static Applications Values of sine, cosine, digression as the proportion of lengths (right triangles) trig tables utilized as a part of computations for edges and lengths sine and cosine laws for general triangles Language of science at the time engaging issues and confirmations utilization of mathematical images seeming last mentioned
Slide 7P theta O ARISTOTELIAN TRIGONOMETRY: Applications in Motion Circle of span 1 unit of decision as trigonometric qualities are lengths trigonometric qualities not proportions but rather elements Sine Cosecant Cosine Secant Tangent Cotangent
Slide 8ARISTOTELIAN TRIGONOMETRY: Applications in Motion Study conduct of trigonometric values as edge changes occasional marvel particularly in mechanics and movement
Slide 9ARISTOTELIAN TRIGONOMETRY: Applications in Motion Needed improvement of variable based math and capacity documentation (Euler) facilitate framework (Descartes) Static versus Motion Trigonometry is this calculated distinction comprehended by understudies? do understudies need to "unlearn" static trigonometry to continue?
Slide 10PLATONIC TRIGONOMETRY Unifying condition of logarithms, trigonometry, complex numbers (Cotes, De Moivre, Euler)
Slide 11PLATONIC TRIGONOMETRY No genuine arrangements. Limitlessly numerous mind boggling arrangements:
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