.
sin θ = 5/6
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If = , then
= +/- = +/- = +/- = +/- = +/- = +/-.
So, by knowing , you can find the modulus (the absolute value) of .
But you can not determine the sign of .
It can be "+" (positive) or "-" (negative).
To determine the sign, you need an additional info.
For example, if you know to which quadrant the angle belongs, then you can determine the sign of ,
and then you know everything.
When you know everything for (and , of course), then you can calculate all other trigonometric functions.