Matematické Fórum

Skrytý text:


As concerns the problem. I believe it comes down to solving these inequations





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To elaborate:

I rewrote sine as cosine and I got a quadratic function on the left (when I substituted ). If the inequality has to hold for every real x, I had to make sure the the roots were not in <-1;1> as that are the values the function can achieve (or reach? what's the correct verb?). For the quadratic function to be negative for all x, one root has to be greater than 1, the other lower than -1.


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Okay, so the first inequality poses no restrictions on us (given the possibilities), the second one is equivalent (again, given the possibilies!) to

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Since the original inequality is strict, the result should be -3, if it wasn't, the answer could be -2 as equality could be achieved for a = -2.

(I hope you didn't mean "largest negative number in absolute value", that would be a different question and the answer would be -4)