Perhaps you can visualize degrees better than radians?
19π/12 radians = 285°
285° is in quadrant IV, so
sin 19π/12 = sin 285°
= - sin(75°) , due to the CAST rule
= - sin(45 + 30)
= -(sin45cos30 + cos45sin30)
= - (√2/2(√3/2) + √2/2(1/2)
= -√6/4 - √2/4
or -(√6 + √2)/4
sin 19pi/12
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