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If csc θ < sec θ is acute, what do you know about θ?
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Double check that you've copied down the problem correctly. It's not correct to state, "csc theta < sec theta is acute." Perhaps you meant to state, "...where theta is an acute angle."
It might prove helpful if y ou were to graph the csc and the sec functions on the same set of axes. Then you could compare the two functions by comparing their graphs. I'd bet that the objective here is to find values of the angle x that satisfy csc theta < sec theta.
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