Cluster+2+Clip+3+Activity+2+Part+1

Scene 2
Explanatory: An angle is sometimes described as having a vertex and two arms. Show two line segments and vertex at 30d. Neither horizontal or vertical. Show continue Explanatory: The arms are sometimes called the initial arm and the terminal arm. The initial arm is where the angle starts and the terminal arm is where is ends. Next to line segment angle put a ray angle at 30d same orientation as the last. Explanatory: Other times an angle is described as having a centre and two rays, the initial ray and the terminal ray. Show Continue Explanatory: The angle is a measure of the rotation required to map the initial ray onto the terminal ray. Have a button called Show Me that animates a copy of the initial ray rotating to the terminal ray leaving a directed arc close to the centre and when done being labeled by Explanatory: Angles are often labeled with Greek letters like Show Continue

Scene 3
Have the line segment angle fade out and leave the angle with the centre, initial ray and terminal ray labeled, with the initial ray not horizontal and the angle less than 90 degrees. Introduce a graphing board that can contain the angle - small scale i.e. -2 to 2

Explanatory Text: To define //sine// for angles bigger than 90d, the angle must be placed in //standard position// in a coordinate system. Instruction: Drag the centre of the angle to the origin of the coordinate system. Feedback: Correct or Incorrect. The origin is where the horizontal and vertical axes meet. (Max three tries) Continue

Instruction: Drag the initial ray of the angle to the positive x-axis. The ray will rotate about the centre until it is considered close enough. Feedback: Correct or Incorrect. The positive x-axis is highlighted. (Max. three tries) Continue

Explanatory: The angle between the initial ray and the terminal ray, in the counterclockwise direction is often denoted by the Greek letter,. Show a directed arc to indicate the angle, Continue

Explanatory: Representing a situation on a coordinate system is a common mathematical strategy. The location of the origin and the axes requires strategic choices. Here we chose to locate the origin at the centre of the angle and one axis along the initial ray of the angle.

Scene 4
Given: Final situation from Scene 3 Explanatory: Any point on the terminal ray of an angle in standard position can be referenced by its coordinates. Instruction: Drag the point on the terminal ray and watch the coordinates change. Have coordinates and dotted lines appear (a la Activity 1 Scene 7). Once they have dragged the point more than 20 pixels show the continue button.

Scene 5
Given: Final situation from Scene 4 Explanatory: Any point on the terminal ray of an angle in standard position can also be referenced by its distance from the origin. Instruction: Drag the point on the terminal ray. Have coordinates and dotted lines appear grayed. Have r=number show up along the terminal ray. Once they have dragged the point more than 20 pixels show the continue button.

Scene 6
Given: A situation like Scene 5 (can be static) with the right triangle situation from Activity 1 Scene 8 animating out of it as a copy Instruction: Compare the angle in standard position to the angle in a right triangle. Fill in the blanks by dragging the correct response. r is like the __.__ _ is like the opposite side.

Have draggable items x,y,r and adjacent side, opposite side, hypotenuse available to be dropped into the blanks. Give feedback when correct or incorrect. When both correct show continue button.

Animate the sequence In a right triangle, sine=opposite/hypotenuse to For an angle in standard position, sine = y/r. The former could be under the triangle and animate to the latter under the coordinate grid.

Scene 7
Given: Standard Position part of Scene 6 diagram, together with new definition for sine. Instruction: Drag the point on the terminal arm to calculate the value of sine.

Like Activity 1, have the values of y and r change and the sine value be calculated (it will not change) Once they have dragged the point, ask the question True or False. The value of sine is the same for any point on the terminal ray of a specified angle. Give Feedback When correct, show the continue button.

Scene 8
Given: Scene 7 diagram for a new angle in the first quadrant and definition of sine Instruction. Use the definition for the sine of an angle in standard position to calculate sin. Note: Dragging the point on the terminal arm to another location may simplify the calculation. Like Activity 1, Scene 3, the user enters the value of sin, gets feedback and the terminal point then is shown in the r=1 position (make something special happen then?) There will be one question for an angle in each quadrant.

Scene 9
Like Activity 1 Scenes 4,5 Given: Angle in standard position with r=1 Instruction. Drag the point on the terminal arm to change the angle. Once that is done, Ask: When r =1, sin has the same value as - x - y - r - using checkboxes from Activity 1. Give feedback and when correct, show the continue button. Instruction: Think: why might the letter //r// be used to label this distance? Show continue Tell that all the positions with r=1 form a circle, with radius 1, called the unit circle.

Part 2