Let x be a real number such that sin(sin x) = 1/2 and 2 < x < 3. What's the value of cos(-sin x)?

The answer is relatively obvious but I cannot for the life of me figure out the need to restrict x to (2,3). The added information does not change what the answer would be if that restriction was not there...at least as far as I can tell.

If there is a reason, I would love to see it!

Thank you in advance.

## Princeton Review, Page 33, Problem 21

### Re: Princeton Review, Page 33, Problem 21

uhhh, I can't see any reason either - I'm gonna chalk this up to an error in the princeton review book, it wouldn't the first.

### Re: Princeton Review, Page 33, Problem 21

I think so too!

In terms of other typos, check out my other post. I've listed one or two.

In terms of other typos, check out my other post. I've listed one or two.

### Re: Princeton Review, Page 33, Problem 21

Could you list the possible answers given in the book? The restriction of x matters because cos(-5pi/6) =/= cos(-pi/6).

### Re: Princeton Review, Page 33, Problem 21

Sin(x) can only be pi/6 as it must be both in the preimage of 1/2 and in the range of sin.

Thus, cos(-sin(x)) = cos(sin(x)) = cos(pi/6).

The restriction on x does not seem to matter.

Thus, cos(-sin(x)) = cos(sin(x)) = cos(pi/6).

The restriction on x does not seem to matter.

### Re: Princeton Review, Page 33, Problem 21

Yeah, you're right.berkbelt wrote:Sin(x) can only be pi/6 as it must be both in the preimage of 1/2 and in the range of sin.

Thus, cos(-sin(x)) = cos(sin(x)) = cos(pi/6).

The restriction on x does not seem to matter.