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Math Help - Find trig functions on unit circle.

  1. #1
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    Find trig functions on unit circle.

    I'm having trouble with this problem. My professor never showed how to get the answers in the key, so I have no idea how to solve these.

    6) Suppose that sinA = 3/5 and tanA<0. Find the following. Clearly explain your reasoning and draw pictures (when appropriate) to help justify your answer.

    a) cosA

    b) tanA

    c) sin(A+pi)

    d) sin(-A)


    Thanks beforehand for the help.
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  2. #2
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    Re: Find trig functions on unit circle.

    Quote Originally Posted by FatimaA View Post
    I'm having trouble with this problem. My professor never showed how to get the answers in the key, so I have no idea how to solve these.

    6) Suppose that sinA = 3/5 and tanA<0. Find the following. Clearly explain your reasoning and draw pictures (when appropriate) to help justify your answer.

    a) cosA

    b) tanA

    c) sin(A+pi)

    d) sin(-A)


    Thanks beforehand for the help.
    What have you been able to do with these?

    -Dan
    Thanks from MarkFL
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  3. #3
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    Re: Find trig functions on unit circle.

    Quote Originally Posted by FatimaA View Post
    6) Suppose that sinA = 3/5 and tanA<0. Find the following. Clearly explain your reasoning and draw pictures (when appropriate) to help justify your answer.
    a) cosA
    b) tanA
    c) sin(A+pi)
    d) sin(-A)

    Recall that if \sin(A)>0~\&~\tan(A)<0 then A\in II.

    Now \sin(A)=\frac{y}{r},~\cos(A)=\frac{x}{r},~\&~r^2=x  ^2+y^2~.

    c) \sin(A+\pi)=-\sin(A).

    d) \sin(-A)=-\sin(A).
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  4. #4
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    Re: Find trig functions on unit circle.

    I haven't been able to get anywhere, really. Looking back through my notes, I get lost. I don't know which identities I'm supposed to use.
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  5. #5
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    Re: Find trig functions on unit circle.

    Quote Originally Posted by FatimaA View Post
    I haven't been able to get anywhere, really. Looking back through my notes, I get lost. I don't know which identities I'm supposed to use.
    Look at reply #3.

    What are x=?~,~y=?~\&~r=~?.

    You must reply with answers in order to get more help.
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  6. #6
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    Re: Find trig functions on unit circle.

    Ok I worked with reply 3. I am supposed to use the even-odd properties? I don't know how you got -sinA from sin(A+pi).

    For d and c, I got -3/5.

    I'm lost on a and b. I don't know how to use the information. My teacher got -4/5 for a but when I attempted it I had -3/5.
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  7. #7
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    Re: Find trig functions on unit circle.

    Quote Originally Posted by FatimaA View Post
    Ok I worked with reply 3. I am supposed to use the even-odd properties? I don't know how you got -sinA from sin(A+pi).

    For d and c, I got -3/5.
    Look, you did not do as I asked you to do.

    What are x=?~,~y=?~\&~r=~?.

    Until you can answer that, there no hope for you to understand this question.

    If you don't want to learn how to do do this, then don't answer.
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  8. #8
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    Re: Find trig functions on unit circle.



    y^2 = (sinA)^2, x^2 = (cosA)^2, r^2 = 1

    x^2+y^2=1

    (3/5)^2+x^2=1

    9/25+x^2=1

    x^2 = -16/25

    x = -4/5
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  9. #9
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    Re: Find trig functions on unit circle.

    Quote Originally Posted by FatimaA View Post

    y^2 = (sinA)^2, x^2 = (cosA)^2, r^2 = 1

    x^2+y^2=1

    (3/5)^2+x^2=1

    9/25+x^2=1

    x^2 = -16/25

    x = -4/5
    NO!
    x=-4~,~y=3~\&~r=~5. Why? is that so? Look at Reply #3 again.

    Answer the questions.
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  10. #10
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    Re: Find trig functions on unit circle.

    sinA = 3/5

    sinA = y/r

    cosA = x/r

    y^2 + x^2 = r^2

    y = 3, r = 5

    3^2 + x^2 = 5^2

    9+ x^2 = 25

    x^2 = 16

    x = 4 but because it's in quadrant II it is -4

    so cosA = -4/5
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  11. #11
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    Re: Find trig functions on unit circle.

    Quote Originally Posted by FatimaA View Post
    sinA = 3/5
    sinA = y/r
    cosA = x/r
    y^2 + x^2 = r^2
    y = 3, r = 5
    3^2 + x^2 = 5^2
    9+ x^2 = 25
    x^2 = 16
    x = 4 but because it's in quadrant II it is -4
    so cosA = -4/5
    Yes, now you have it.
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