1. ## two simple questions.

suppose u is an angle in the second quadrant and sin u=2/3.
i need to find cos u and tan u. and then what u is.
cos u= -sqrt (5/9)
tan u= (2/3)/ (-sqrt (5/9))
but i cant figure out what u is. i thought it would be just arc sin of 2/3 but i keep getting the wrong answer. oh and it wants the answer in radians.

my second question is cos (3x)=1/2. i need to find the two solutions between 0 and 120. i found that arc cos 1/2=3x so that x=20 and then i just guessed and found that the second answer is 100 degrees. but i dont know why....

i hope someone can help !! thanks a bunch!!

2. [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, u lies 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.

3. oh wow yeah i get it. knowing those two identities defitnetly helps. Thanks a lot!!!