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Math Help - trig questions

  1. #1
    Newbie
    Joined
    Nov 2005
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    6

    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!!
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  2. #2
    Member
    Joined
    Nov 2005
    From
    Wethersfield, CT
    Posts
    92
    [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.
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  3. #3
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    Joined
    Nov 2005
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    oh wow yeah i get it. knowing those two identities defitnetly helps. Thanks a lot!!!
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