10.3.A 9&11

I somehow managed to get the answers switched around for 9 and 11: the answer i got for 9 is listed in the textbook as the answer to 11 and vice versa. For 11, i got cot(2*theta) = (17-31)/48, which simplifies to -7/25. plugging -7/25 into the half-angle identities, I got that sine of theta is the square root of (1- -7/25)/2, which comes out to 4/5, making the cosine 3/5. but the answer in the book has the sine and cosine values switched around. Same goes for number 9, which has the cotangent of the double angle equal to positive 7/25. can someone tell me what i'm doing wrong (assuming the book isn't wrong)?