[SIZE=2]Hi Elizabeth:

The problem with your answer arcsin(2/3), i.e. 0.730 radians to three places, is that an angle measuring at 0.730 radians (41.8 deg.) lies in the first quadrant. But, according to your post,ulies in quadrant II. To remedy this problem, we must find a 2nd quadrant angle with sine also equal to 2/3. It will likely serve you well to commit the following identity to memory. Sin(pi-x) = sin(x) [equivalently, sin(180-x)=sin(x) for degree measured angles] So, sin(u)=sin(pi-0.730). Clearly, pi-0.730, i.e., 2.41 radians [138 deg] lies in Q2. Thus, u=2.41 to two places.

Re. question 2, cos(3x)=0.5 indeed implies 3x=60 deg. But what other angle has cosine = 0.5? We have another identity stating that cos(t)=cos(2pi-t). Therefore, cos(60)=cos(360-60) or, cos(300). The result is: 3x=60, 3x=300 which implies x=20, x=100.

In the morning, I will supplement this post with more information that should clear up remaining confusion.

Regards,

Rich B.