Back to school… (a) Examine the impact of the parameters on the graph of the sine functions by changing the values of the sliders. (b) Set a1 = 1, = 1 and = 0. For which values of and does ω1 φ1 a2, ω2 φ2 the sum have maximal amplitude? Note: In this case the resulting tone has the maximal volume. (c) For which values of a2, and do the two functions cancel each ω2, φ2 other? Note: In this case no tone can be heard any more. Introducing Derivatives – The Slope Function In this activity you are going to use the following tools, algebraic input, and commands. Make sure you know how to use them before you begin with the actual construction. f(x) = x^2/2 + 1 S = (x(A), m) Point Segment Tangents Move m = Slope[t] Hint: You might want to have a look at the link to the dynamic worksheet Derivatives - The Slope first. “Introducing Function” Preparations Open a new GeoGebra window. Switch to Perspectives - Algebra & Graphics. Introduction of new tool New! Tangents Hint: Click on a point on a function and then on the function itself. Hints: to read the Toolbar help if you know how to use the tool. Don’t forget don’t Try out the new tool before you start the construction.
Back to school… (a) Examine the impact of the parameters on the graph of the sine functions by changing the values of the sliders. (b) Set a1 = 1, ω1 = 1 and φ1 = 0. For which values of a2, ω2 and φ2 does the sum have maximal amplitude? Note: In this case the resulting tone has the maximal volume. (c) For which values of a2, ω2, and φ2 do the two functions cancel each other? Note: In this case no tone can be heard any more. Introducing Derivatives – The Slope Function In this activity you are going to use the following tools, algebraic input, and commands. Make sure you know how to use them before you begin with the actual construction. f(x) = x^2/2 + 1 S = (x(A), m) Point Segment Tangents Move m = Slope[t] Hint: You might want to have a look at the link to the dynamic worksheet “Introducing Derivatives - The Slope Function” first. Preparations Open a new GeoGebra window. Switch to Perspectives - Algebra & Graphics. Introduction of new tool Tangents New! Hint: Click on a point on a function and then on the function itself. Hints: Don’t forget to read the Toolbar help if you don’t know how to use the tool. Try out the new tool before you start the construction.
ggb-intro-en44-2014-07-17.docx