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

Guest Nov 29, 2020

#2**+1 **

Various multiples of pi/4 make sin^{2}(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(sin^{2}(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.

Alan Nov 29, 2020