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suppose theta is in the interval (90,180 degrees) find the sign of

csc(-theta)

is it positive or negative

= positive???

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-theta is in quadrant 3, lower left
In that quadrant the sin is negative so the csc is negative.
for example if theta = 150 deg
then -theta = -150
and csc(-150) = 1/-.5 = -2

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