Princeton Review, Page 33, Problem 21

Forum for the GRE subject test in mathematics.
berkbelt
Posts: 15
Joined: Sun Jun 02, 2013 12:19 pm

Princeton Review, Page 33, Problem 21

Postby berkbelt » Sat Jul 06, 2013 6:08 pm

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.

ahfats37
Posts: 3
Joined: Sat Nov 10, 2012 3:52 pm

Re: Princeton Review, Page 33, Problem 21

Postby ahfats37 » Mon Jul 08, 2013 4:24 pm

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.

berkbelt
Posts: 15
Joined: Sun Jun 02, 2013 12:19 pm

Re: Princeton Review, Page 33, Problem 21

Postby berkbelt » Tue Jul 09, 2013 10:18 am

I think so too!

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

Ryker
Posts: 74
Joined: Mon Jul 08, 2013 11:27 pm

Re: Princeton Review, Page 33, Problem 21

Postby Ryker » Wed Jul 10, 2013 1:40 am

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

berkbelt
Posts: 15
Joined: Sun Jun 02, 2013 12:19 pm

Re: Princeton Review, Page 33, Problem 21

Postby berkbelt » Wed Jul 10, 2013 9:04 am

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.

Ryker
Posts: 74
Joined: Mon Jul 08, 2013 11:27 pm

Re: Princeton Review, Page 33, Problem 21

Postby Ryker » Wed Jul 10, 2013 12:35 pm

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.
Yeah, you're right.




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