Answer :
The y-coordinate of point P on the unit circle in quadrant IV with cos(t) = (13/15) is -2 * sqrt(14)/15.
To find the y-coordinate of point P that lies on the unit circle in quadrant IV, where cos(t) = (13/15), we must use the Pythagorean identity sin^2(t) + cos^2(t) = 1 for a unit circle. Since P lies in quadrant IV, the sin(t) must be negative because sine is negative in that quadrant.
First, we calculate sin^2(t):
- sin^2(t) = 1 - cos^2(t) = 1 - (13/15)^2 = 1 - (169/225) = (225/225) - (169/225) = 56/225
Then we find sin(t):
- sin(t) = -sqrt(56/225)
- sin(t) = -sqrt(56)/15
- sin(t) = -sqrt(4 * 14)/15
- sin(t) = -2 * sqrt(14)/15
Thus, the y-coordinate of point P is -2 * sqrt(14)/15.