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Answer :
The y-coordinate of the point P on the unit circle in quadrant IV, given that cos(t) = (13/15), is -2√14/15.
To find the y-coordinate of the point P on the unit circle corresponding to an angle of t, where cos(t) = (13/15) and P is in quadrant IV, we use the Pythagorean identity sin2(t) + cos2(t) = 1. Since cos(t) is given, we can solve for sin(t), which corresponds to the y-coordinate.
We have cos2(t) = (169/225). Therefore, sin2(t) = 1 - (169/225) = (225/225) - (169/225) = (56/225). Since we are in quadrant IV, we should take the negative square root of (56/225) because sine is negative in this quadrant. Thus, sin(t) = -√(56/225) which simplifies to -(2√14)/15.
The y-coordinate for point P is therefore -2√14/15.
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