To find the y-coordinate of point P on the unit circle, given that its x-coordinate is 5/13, we can utilize the Pythagorean identity for points on the unit circle.
The Pythagorean identity states that for any point (x, y) on the unit circle, the following equation holds true:
x^2 + y^2 = 1
Since we are given the x-coordinate as 5/13, we can substitute this value into the equation and solve for y:
(5/13)^2 + y^2 = 1
25/169 + y^2 = 1
To isolate y^2, we subtract 25/169 from both sides:
y^2 = 1 - 25/169
y^2 = 169/169 - 25/169
y^2 = 144/169
Taking the square root of both sides, we find:
y = ±sqrt(144/169)
Since we are dealing with points on the unit circle, the y-coordinate represents the sine value. Therefore, the y-coordinate of point P is:
y = ±12/13
So, the y-coordinate of point P can be either 12/13 or -12/13.
♥️
