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?

Question

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?

amistre64 · Answer

sin inverse and cosine inverse have different ranges

amistre64 · Answer

or domains really, ranges are good  lol

amistre64 · Answer

the domain for the sin:

-pi/2 all the way to pi/2

the domain for the cos:

0 all the way to pi

anonymous · Answer

Ohhhhh I see! Thanks a bunch!!

anonymous · Answer

But why is it not 5pi/3?

anonymous · Answer

Th first one is -pi/3, isn't that the same as 5pi/3? So why is the reference radian used?

amistre64 · Answer

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.

amistre64 · Answer

to keep these inverses a function....is what it was sposed to say

amistre64 · Answer

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 ;)

anonymous · Answer

Ohhhh I get that! Thanks heaps!

amistre64 · Answer

youre welcome :)