Determining Theta in Sin Ratio: Why the Difference?

[supernova1203]

Homework Statement

The ratio sin theta =-12/13

Homework Equations

The Attempt at a Solution

which comes out to according to my calcuations -0.9230, i then use 2nd sin function on my calculator and come up with -67.3 degrees

this answer is legitimate but another way of writing it would be 180-67.3 degrees
which is 112.7 degrees
180-67.3
=112.7

but the book for some reason shows sin theta = 12/13, it removes the negative on the 12 value when it does the 2nd sin function on calculator(atleast that's what it looks like) why does it do this?

the books answer comes out to be
theta= 180+ 67.3
=247.3

so the plus and minus is what is different about my solution and books. it could be a typo, there have been many in my course book @_@

 

[HallsofIvy]

Is the question to find theta? And how old is this book?

Once upon a time, in the years B.C. (Before Calculators), you used to have to look up sines and arcsines in tables. And, to save room, those tables only gave angles from 0 to 90 degrees (other angles duplicate those values). Of course, the sine of any angle between 0 and 90 degrees is positive. So to find theta for a negative sine, you look up the "reference angle" for the positive value- then correct for the sign. In order to have a negative sine, the angle must be between 180 and 360 degrees. There are, actually, two different angles between18 0 and 360 degrees that give a specific negative sine- one is 180 plus the reference angle, the other is 360 minus the reference angle.

180- 67.3 would be between 0 and 180 and would have positive sine. Since your calculator gave you "-67.3", to get an angle between 0 and 360, you should use either 360- 67.3 or 180+ 67.3.