How can transformations be represented Exploration, through the use of graphing trigonometrically? technology and interactive geometry, of the effect of: Horizontal and vertical dilations, translations, vertical dilations on the equation and and/or reflections, and their effect on amplitude of trigonometric functions trigonometric functions and their graphs, including a brief treatment of all three reciprocal horizontal dilations on the equation and period functions: of trigonometric functions vertical translations on the equation and range of trigonometric functions horizontal translations on the equation and range of trigonometric functions reflection in the on the equation and graph of trigonometric functions. The graphs and periodicity of the reciprocal trigonometric functions can also be considered using electronic technology. Subtopic 1.3: Trigonometric Identities Key Questions and Key Ideas Considerations for Developing Teaching and Learning Strategies What trigonometric identities for sine and cosine Students derive the formula for by the dot functions are used? product (see Subtopic 13.9 of Stage 1 Mathematics). Students compare this derivation Addition formulae with the approach using the cosine rule Double angle formulae (see Subtopic 14.7 of Stage 1 Mathematics). The other addition formulae are derived using the properties established in Subtopic 1.1. The identity could be considered at this point for later use in Topic 4: Calculus. Topic 2: Polynomials and Complex Numbers Subtopic 2.1: Complex Numbers Key Questions and Key Ideas Considerations for Developing Teaching and Learning Strategies
How can transformations be represented trigonometrically? Horizontal and vertical dilations, translations, and/or reflections, and their effect on trigonometric functions and their graphs, including a brief treatment of all three reciprocal functions: Exploration, through the use of graphing technology and interactive geometry, of the effect of: vertical dilations on the equation and amplitude of trigonometric functions horizontal dilations on the equation and period of trigonometric functions vertical translations on the equation and range of trigonometric functions horizontal translations on the equation and range of trigonometric functions reflection in the on the equation and graph of trigonometric functions. The graphs and periodicity of the reciprocal trigonometric functions can also be considered using electronic technology. Subtopic 1.3: Trigonometric Identities Key Questions and Key Ideas Considerations for Developing Teaching and Learning Strategies What trigonometric identities for sine and cosine functions are used? Addition formulae Double angle formulae Students derive the formula for by the dot product (see Subtopic 13.9 of Stage 1 Mathematics). Students compare this derivation with the approach using the cosine rule (see Subtopic 14.7 of Stage 1 Mathematics). The other addition formulae are derived using the properties established in Subtopic 1.1. The identity could be considered at this point for later use in Topic 4: Calculus. Topic 2: Polynomials and Complex Numbers Subtopic 2.1: Complex Numbers Key Questions and Key Ideas Considerations for Developing Teaching and Learning Strategies