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## a1234 one year ago Function value: csc theta = 4 Constraint: sin theta < 0 Find tan theta. Is it -((sqrt15)/15)?

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1. anonymous

$\sin ~ and~ \csc ~have~same~sign.$ $\csc ^2 \theta-\cot ^2 \theta=1$ $4^2-\cot ^2\theta=1$ $\cot ^2\theta=16-1=15$ $\tan ^2\theta=\frac{ 1 }{ 15 }$ $\sin \theta <0,means ~\theta~lies ~\in~3rd~or~4th~quadrant.$ if in 3rd quadrant tan theta is positive If in 4th quadrant tan theta is negative.

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