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Find the smallest positive integer $x$ for which the expression log(sin^2(x) - 1/2) is not defined. (The sine function is evaluated in terms of radians.)

 

Where I am stuck: I don't know what to do to make sin^2(x) = to 1/2.

 

what I found: after experiment with log, I found that log_0 2 or anything is undefined, therefore 0^x=2, so that is undefined. therefore sin^2(x) is 1/2, so that the expression is equal to 0

 Nov 29, 2020
 #1
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I'm getting an answer of x = 6.

 Nov 29, 2020
 #2
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Various multiples of pi/4 make sin2(x) - 1/2 = 0.   However, none of these result in x being an integer!

 

If the question is restricted to real numbers, then the argument to the log function must simply be positive.  In this case, log(sin2(x)-1/2) is ok for x = 1 and 2, but is complex for x = 3, so x = 3 would be the smallest positive integer.

 Nov 29, 2020

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