Final answer:
To show that a point is on the unit circle, we need to check if its coordinates satisfy the equation x^2 + y^2 = 1. The point (5/13, 12/13) is on the unit circle, while (√pi/6, 5/6) is not.
Step-by-step explanation:
To show that a point is on the unit circle, we need to check if its coordinates satisfy the equation x^2 + y^2 = 1. Let's consider the given points:
(a) (5/13, 12/13)
Substituting the values into the equation, we get (5/13)^2 + (12/13)^2 = 25/169 + 144/169 = 169/169 = 1.
Therefore, the point (5/13, 12/13) is on the unit circle.
(b) (√pi/6, 5/6)
Substituting the values into the equation, we get (√pi/6)^2 + (5/6)^2 = pi/36 + 25/36 = (pi + 25)/36.
Since (pi + 25)/36 is not equal to 1, the point (√pi/6, 5/6) is not on the unit circle.