Actually if the question does not specify they should accept both answers, and there are a multitude of other answers they should accept. If you ever write an answer that is right and the question does not specify which quadrant or range, you can debate it with the graders. But most of the time, put the least value because that is what the answer key will have and there is no reason in debating something if you know what the answer is supposed to have.
As for the second question, you need to remeber that csc(x) is the same as 1/sin(x) and also remember that sin(-x) = sin(x). So if sin(x) = 10/11 the csc(-x) = 1/sin(-x) = 1/10/11 = 11/10 or 1.1. It is not negative. If the question had been:
lol, thanks, happy new year to you too. yeah it's a big holiday in china, my new year resolution is to place in state this yr in ns so our team can have a bigger budget in my senior year
On a Number Sense test they are usually asking for principal solutions. The inverse cosine and the inverse sine are capitalized. In this situation, if they are asking for the inverse cosine the angle must be between 0° and 180°, inclusive. If they are asking for inverse sine the angle must be between - 90° and 90°. Invcos 1/2 = 60° and Invsin 1/2 = 30°. In Invcos and Invsin are not capitalized they are looking for the general solution. They will never ask for the general solution on a Number Sense test.
