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  1. #1
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    domain

    the function f(x)=ln(sinx) is defined for all x in which of the following intervals?
    a) 0<x<pi
    b)0<= x <= pi
    c) 3pi/2<x<5pi/2
    d)3pi/2 <= x <= 5pi/2
    e) 3pi/2<x< 2pi
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Ok

    Quote Originally Posted by sandiego234 View Post
    the function f(x)=ln(sinx) is defined for all x in which of the following intervals?
    a) 0<x<pi
    b)0<= x <= pi
    c) 3pi/2<x<5pi/2
    d)3pi/2 <= x <= 5pi/2
    e) 3pi/2<x< 2pi
    I will give you a big hint ln(u(x)),u(x)>0...so find the interval on which sin(x)>0 and you have yoru partial domain
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  3. #3
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    is it A?

    please verify. thank you.

    0 would give sin0=0
    sin pi= 0
    sinpi/3= root3/2
    sinpi/2 = 1
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  4. #4
    GAMMA Mathematics
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    Quote Originally Posted by sandiego234 View Post
    the function f(x)=ln(sinx) is defined for all x in which of the following intervals?
    a) 0<x<pi
    b)0<= x <= pi
    c) 3pi/2<x<5pi/2
    d)3pi/2 <= x <= 5pi/2
    e) 3pi/2<x< 2pi
    Think, -1 \le sin(x) \le 1 AND 0 \ge ln(x), but to get positive values of sine, then it must be in the 1st and 2nd quadrants, or 0 \le x \le \pi
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  5. #5
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    are you sure this is right?

    if it were to be 0<= x<= pi
    then sin pi is zero, meaning ln(0)= undefined....
    also sin(0)= 0, meaning ln(0)
    that would not be part of the domain therefore.
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