Sine-Cosine Relationship on Unit Circle

This activity intends to start exploring how the trigonometric ratios of an angle in one quadrant relate to the trigonometric ratios of a related angle in a neighboring quadrant. From there, trigonometric identities may be constructed and the relationship between sinusoidal functions may be understood more deeply.
Note that [color=#ff00ff]α[/color] is the central angle measure corresponding to point [color=#ff00ff]A[/color] on the unit circle and [color=#6aa84f]β[/color] is the measure of the central angle corresponding to point [color=#6aa84f]B[/color].[br][br][b](1)[/b] Look at the GeoGebra construction and observe the 
relationship between [color=#ff00ff]α[/color] and [color=#6aa84f]β[/color]. Write an equation describing this relationship (using radians, not degrees).
[b](2)[/b] Note that the sides of triangle '[color=#6aa84f]B[/color]' are labeled with variables [color=#0000ff]p[/color], [color=#0000ff]q[/color], and [color=#0000ff]r[/color]. Label the sides of triangle '[color=#ff00ff]A[/color]' with those same [color=#0000ff]variables[/color], observing any + and −. Then evaluate sine, cosine, and tangent for both [color=#ff00ff]α[/color] and [color=#6aa84f]β[/color] in terms of these variables.
[b](3)[/b] Which trigonometric ratio of [color=#ff00ff]α[/color] is equal to which trigonometric ratio of [color=#6aa84f]β[/color]? Write an equation stating this.
[b](4)[/b] Substituting in the equation from step 1, write the equation from step 3 in terms of a single variable.
[b](5)[/b] Give an example of this relationship that 
you can verify on your calculator. Does this relationship hold for all values of [color=#ff00ff]α[/color] and [color=#6aa84f]β[/color]? [br][br]
[b](6)[/b] Using the language of graphical transformations, examine the equation from step 4 and explain how the graph of [i]y[/i] = sin [i]x[/i] relates to the graph of [i]y[/i] = cos [i]x[/i].[br][br]
Fermer
– talljerome

Information: Sine-Cosine Relationship on Unit Circle