Why is sin^-1 (-sqrt3/2) = -pi/3 and cos^-1 (-sqrt2/2) = 3pi/4 Basically, why in the first problem is the answer a negative reference angle and the second one is not?

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Why is sin^-1 (-sqrt3/2) = -pi/3 and cos^-1 (-sqrt2/2) = 3pi/4 Basically, why in the first problem is the answer a negative reference angle and the second one is not?

Mathematics
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sin inverse and cosine inverse have different ranges
or domains really, ranges are good lol
the domain for the sin: -pi/2 all the way to pi/2 the domain for the cos: 0 all the way to pi

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Ohhhhh I see! Thanks a bunch!!
But why is it not 5pi/3?
Th first one is -pi/3, isn't that the same as 5pi/3? So why is the reference radian used?
5pi/3 is not in the domain of the sin inverse function; but, its equivalent "-pi/3" is. So to these inverse a "function" meaning that for every single input there can only be one output, they have to give an answer to a restricted domain.
to keep these inverses a function....is what it was sposed to say
for example: which would you rather have: $20 in as one 20 dollar bill? or in 20 one dollar billls? both are equaivalent amounts, but if all you got is ones, then thats all you get ;)
Ohhhh I get that! Thanks heaps!
youre welcome :)

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