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    Doglover2011's Avatar
    Doglover2011 Posts: 16, Reputation: 1
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    #1

    Oct 7, 2009, 11:35 AM
    Finding Trig. Functions, almost done but got stuck?
    I'm trying to study for an upcoming test and was doing this problem:

    Find the values of the other five trig functions given that sin= 1/2, pi/2<Theta<Pi

    I have found all but 2 functions, Tan and Cot. I am not sure which formula to use for this. Any suggestions?
    Unknown008's Avatar
    Unknown008 Posts: 8,076, Reputation: 723
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    #2

    Oct 7, 2009, 11:39 AM

    I don't quite understand what you have to do. Could you post the answers you already got?
    Doglover2011's Avatar
    Doglover2011 Posts: 16, Reputation: 1
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    #3

    Oct 7, 2009, 12:01 PM

    We have to find the other functions-sine, cosine, etc.

    Here are my answers(I hope they are right hehe but I think they are):

    Sine-1/2
    Csc-2
    Cos-square root of 3/2
    Sec-2times square of 3/3

    Now I just need to figure out how to get Tan, because Cot will be the recp. Of Tan. I need to use an identity, I just don't know which one. I don't see any with just sine and Tan.
    Doglover2011's Avatar
    Doglover2011 Posts: 16, Reputation: 1
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    #4

    Oct 7, 2009, 12:03 PM
    and we are suppose to use the given (1/2 sine) to figure it out.

    But I wonder if I could use

    Sin(1/2)^2+Cos^2Theta=1?
    ArcSine's Avatar
    ArcSine Posts: 969, Reputation: 106
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    #5

    Oct 7, 2009, 12:53 PM
    Be careful with your signs. The fact that the angle lies between and tells you you're dealing with a Quad II angle. Sine is certainly positive there, but cosine is..

    As to Tan, just remember that by definition . So once you've got sine and cosine in hand, tan is a cakewalk. After that, nail down the other three using the reciprocal identities.

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