Cluster+2+Clip+3+Activity+2+Part+2

Scene 10
Given an angle in standard position, with x,y,r,  labeled and a point on terminal arm with r=1 Instruction: Drag the point to create a table of values for sin from 0d to 360d. As the point is dragged past special values, they are recorded in the table. Do this twice - once for multiples of 45 and again for 30, 60, 120,... (different colours) When they are all there, the continue button shows.

Scene 11
Given the table of values from Scene 10. (You will need to hard code this table in case someone jumps directly to this scene) A button with Plot the points is displayed (a la Activity 1, Scene 8) which plots the points on a graphing board. The table of values disappears and the angle in standard position appears Instruction. Drag the point on the terminal arm to plot more of the sine curve. As the point is dragged the curve is formed (a la Activity 1, Scene 7, Frame 82) Display the sine curve on (0,360). Ask if it is quadratic (a la Activity 1 Scene 8) Once correct, ask them to think about what the curve looks like for angles bigger than 360d and less than 0d.

Scene 12
Given an angle in standard position, and graphing board from Scene 12 Show an animation for first 360d and ask them to rotate more ccw Explanatory: To generate values for angles bigger than 360d, the terminal arm is rotated in a complete revolution counterclockwise and then rotated some more. Instruction: Rotate the terminal arm counterclockwise to generate values bigger than 360. Action: As the terminal arm is rotated once and then some more, the curve is added to. Go to 720d.

Scene 13
Given an angle in standard position, and graphing board from Scene 11 Explanatory: To generate values for angles less than 0d, the terminal arm is rotated in a clockwise direction. Instruction: Rotate the terminal arm clockwise. Action: As the terminal arm is rotated back to -360d the curve grows in that direction. Once done, ask them to think about whether the sine curve is periodic.

Scene 14
An animation that has a red point rotating counterclockwise and a blue point rotating clockwise generating a sine curve with a progressively bigger domain. Explanatory: By placing angles in standard position and using the sine = y/r definition, a curve can be obtained defined for all real values of theta. This curve is periodic, since the same y and r values are used over and over every 360d.

Scene 15
This is part of the graph of y=sin. The letters used for the independent and dependent variables are arbitrary. The axes can be relabeled x and y to get the graph of y = sin x. Here (x,y) is a point on the graph and not a point on the terminal arm of an angle, x, on some coordinate system.