Question

Suppose that (x, (15/17)) is a point in quadrant lying on the unit circle.

Find . Write the exact value, not a decimal approximation.

Answer 1

Which quadrant is it in?

Answer 2

Since the y coordinate is positive, we know it will be in the first or second quadrant.

Answer 3

Either way, we can solve this by using the fact that: \[
x^2 + \left(\frac{15}{17}\right)^2 = 1^2
\]

Answer 4

But unless we get the quadrant, all we can say is that: \[
|x| = \sqrt{1^2-\left(\frac{15}{17}\right)^2}= \sqrt{\frac{17^2-15^2}{17^2}} = \frac {8}{17}
\]