Sine-Cosine Relationship on Unit Circle

Note that α is the central angle measure corresponding to point A on the unit circle and β is the measure of the central angle corresponding to point B. (1) Look at the GeoGebra construction and observe the 
relationship between α and β. Write an equation describing this relationship (using radians, not degrees).

(2) Note that the sides of triangle 'B' are labeled with variables p, q, and r. Label the sides of triangle 'A' with those same variables, observing any + and −. Then evaluate sine, cosine, and tangent for both α and β in terms of these variables.

(3) Which trigonometric ratio of α is equal to which trigonometric ratio of β? Write an equation stating this.

(4) Substituting in the equation from step 1, write the equation from step 3 in terms of a single variable.

(5) Give an example of this relationship that 
you can verify on your calculator. Does this relationship hold for all values of α and β?

(6) Using the language of graphical transformations, examine the equation from step 4 and explain how the graph of y = sin x relates to the graph of y = cos x.