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Assume the angle u takes place in Quadrant IV.
Let u = arctan(-12). Then, tan(u) = -12.
By the Pythagorean identity, we obtain:
sec(u) = √(1 + tan²(u))
= √(1 + (-12)²)
= √145
Since secant is the inverse of cosine, we have:
cos(u) = 1/√145
Therefore:
sin(u) = -√(1 - cos²(u))
= -√(1 - 1/145)
= -12/√145
Otherwise, if the angle takes place in Quadrant II, then sin(u) = 12/√145
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