[b] The unit circle is a circle, [/b]C, of radius 1, centered at the origin (0,0).[br]As we move up line L, we are going to imagine [b]wrapping[/b] the line around C.[br]The value of t becomes the [b]length [/b]of the [b]arc[/b] which has been wrapped around C.[br]Since this is a circle of radius 1[br][list][*][b]wrapping[/b] around the [b]whole circle[/b] ([math]360^o[/math]) would require a length of [math]2\pi[/math].[/*][*][b]wrapping[/b] around half the circle ([math]180^{\circ}[/math]) would require a length of [math]\pi[/math].[/*][/list][br]You can zoom in and out to see higher values of arc length and degrees.[br][br]Every point on the line L corresponds to a point on the circle. This is called the [b]wrapping function[/b].

[left]1. Click on the degrees, and click off the Arc Length and Right Triangle. [br][/left]2. Move the point [i]t[/i] up and down the line. Observe the x and y coordinates. [br]3. Click on right triangle and click off arc length and degrees. [br][br]4. Use the right triangle to find the sin([math]\theta[/math]), cos([math]\theta[/math] where [math]\theta[/math] is the angle from the positive x axis to the point on the unit circle (not the angle in green. How are the sine and cosine related to the x and y coordinates? [br]