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Unit Circle: Complementary Angles

This sketch shows the relationship between an angle and its complement, . Drag around the circle and notice what happens to . How are the trigonometric ratios of the angles related?


What is the geometric relationship between and ?


The coordinates of are . From the relationship described in question 1, what are the coordinates of ?


Since is a point on the unit circle corresponding to the angle in standard position, it has coordinates:

Therefore, for any angle , we have: