Question

The observations you made in the unit circle can help you determine the x‑ and y‑coordinates of special points on the circle without memorizing the circle. Analyze some of the patterns by completing the parts below.

a. Look at all the ordered pairs whose angles are of the form k pi/4, where k is an integer. What do you notice?
b.Now look at the ordered pairs whose angles are of the form k pi/6 or k pi/3. What do you notice about their coordinates?
c.How can you determine if the coordinates of a point are positive or negative?

Answer 1

a. Look at all the ordered pairs whose angles are of the form k pi/4, where k is an integer. What do you notice? These ordered pairs would be found along the lines that make 45 deg, 135 deg, 225 deg and 270 deg angles as measured from the positive x-axis. Every such line is made up of an infinite number of dots representing such pairs. And the x- and y-components of these pairs would be equal in magnitude (but could have different signs).