I don't understand what I should calculate if is said: "find the unique x", e.g. in the following exercise:
"Find the unique x in the interval [0,pi] with cos(x) = 0,5 * sqrt(3)"
$\endgroup$ 12 Answers
$\begingroup$The question is asking to find the $x$ value in $[0,\pi]$ which satisfies $\cos x = \sqrt3/2$. Basically, you're told there is some number $x$ between $0$ and $\pi$ and the cosine of that number is $\sqrt3 /2$ and the question is to determine what this $x$ is. Since there is one (which the question sort of allows you to assume) they use the word "unique". But a look at the unit circle reveals that this unique $x=\pi/6$.
$\endgroup$ $\begingroup$"find the unique $x$" means
1, Such $x$ must exist;
2, it is the only one.
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