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Unit 5 Review Modeling Periodic Functions Periodic Phenomena Vocabulary: cycle, period, axis of the curve, amplitude Angles Vocabulary: ray, vertex, initial arm, terminal arm, standard position, positive angle, negative angle, quadrants of the x-y plane, coterminal angles, principal angle, related acute angle. Trigonometric Functions - Beyond Triangles Example: Point P(4,-3) is on the terminal arm of an angle in standard position. a. Sketch the principal angle, θ. b. Determine the value of the related acute angle to the nearest degree. c. What is the measure of θ to the nearest degree? Special Triangles Example: Find sin 300E without using a calculator. The Unit Circle and Basic Sine and Cosine Graphs Any point P(x,y) on the unit circle can be expressed as the ordered pair (cos θ, sin θ). Transformations Modelling Periodic Phenomena a: d: The amplitude of the curve - ½ total height or distance from middle to top The equation for the axis of the curve - split curve in half horizontally. For sin2 it is y = 0, so the axis of a transformed curve, y = d, gives the vertical translation, d. k: The horizontal stretch/compression – the number of cycles that fit into one cycle of the original sin or cos graph k = b: HW: 360 new period and new period = 360 k To figure out b, the phase (horizontal) shift, refer to the transformed graph: Where have the “starting points” ended up - (0,0) for sin 2 and (0,1) for cos 2? p 485 #1-6, 7a, 8-14, 16, 27 (with 30E instead of π/6), 30ab, 31-33 p 550 #13, 17