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Math Help - Radians

  1. #1
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    Radians

    Hi, need help understanding 2 problems.

    Give all the solutions to the following problems, answer in radians.

    \sin(3x)=\sqrt{3}/2

    and

    \cos(x-pi/4)=1/\sqrt{2}


    Thanks.
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  2. #2
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    Quote Originally Posted by Smifsret View Post
    Hi, need help understanding 2 problems.

    Give all the solutions to the following problems, answer in radians.

    \sin(3x)=\sqrt{3}/2

    and

    \cos(x-pi/4)=1/\sqrt{2}


    Thanks.
    You need to know what angle for sine gives the value \frac{\sqrt{3}]{2}. This happens to be \frac{\pi}{3}

    Solve for 3x = \frac{\pi}{3}
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  3. #3
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    Thanks, is the second one pi / 4 then?

    Does pi/4 count as an answer (if its right) or do they want me to write a number?
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  4. #4
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    sin(3x)= pi/3

    x1. sin(x) = pi/9 + 2 * pi * n?
    x2. sin(x) = pi-pi/9 + 2 * pi * n?



    Is that correct?
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  5. #5
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    Ahh the question is to answer EXACTLY in radians and I was told it isn't exactly unless you write it like that.

    Also the formula + n * 2 * pi I was told to add because n is the number of times it has gone around the circle.

    Hope I explained that decently.


    But I understand that I shouldn't have addad sin to the solution, thank you, as always I wasn't aware that it mattered.
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  6. #6
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    For the second part

    x1 = pi/2

    x2 = -pi/2

    Correct?
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  7. #7
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    Quote Originally Posted by Smifsret View Post
    Ahh the question is to answer EXACTLY in radians and I was told it isn't exactly unless you write it like that.

    Also the formula + n * 2 * pi I was told to add because n is the number of times it has gone around the circle.

    Hope I explained that decently.


    But I understand that I shouldn't have addad sin to the solution, thank you, as always I wasn't aware that it mattered.
    I'm sorry, I should have realized that your x1 and x2 were solutions to the first problem, not solutions to problems 1 and 2.

    In that case, yes, those solutions are correct (with x replacing your sin(x).)

    -Dan
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  8. #8
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    You wrote that
    x - \frac{\pi}{4} = \frac{\pi}{6}
    i think that its
    1/\sqrt{2}=0.70711 = 45  degrees  =  \frac{\pi}{4}


    Or am I completely wrong?
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  9. #9
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Smifsret View Post
    You wrote that
    x - \frac{\pi}{4} = \frac{\pi}{6}
    i think that its
    1/\sqrt{2}=0.70711 = 45  degrees  =  \frac{\pi}{4}


    Or am I completely wrong?
    My apologies again. You are correct.

    I'm going back to bed.

    -Dan
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  10. #10
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    Thank you very much for the help, does that mean that my previous answers were correct?
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