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Math Help - Simple Sector Question

  1. #1
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    Cool Simple Sector Question

    Kindly look at the attached past paper question from British A Level Mathematics.

    1) What I want to know is that since it doesn't state in the question whether to calculate the values of the sectors and arc lengths by using the angles in degrees or radians, if I calculate my answers with angles in degrees (since in the question an angle, 90, is already given in degrees) would my answers be correct/acceptable?

    2) Do we always calculate the values in such sector based questions based upon radians or does the examiner define whether to use degrees or radians.
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  2. #2
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    simple sector problem

    [quote=unstopabl3;509160]Kindly look at the attached past paper question from British A Level Mathematics.

    1) What I want to know is that since it doesn't state in the question whether to calculate the values of the sectors and arc lengths by using the angles in degrees or radians, if I calculate my answers with angles in degrees (since in the question an angle, 90, is already given in degrees) would my answers be correct/acceptable?

    2) Do we always calculate the values in such sector based questions based upon radians or does the examiner define whether to use degrees or radians.[/quote

    Hi unstopabl3,
    Given a problem using degrees why would you want to complicate it.
    Calculate AB. This is a radius of a larger circle centered @ A Complete the quarter circle from D to B0 extended creating a full sector and segment calculate the full sector and subtract the sector triangle. divide this segment area in half for the required area and do the same for lenght of arc BD


    bjh
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  3. #3
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    So we can calculate the values by using degrees in such questions? I have done the question already but as I had used degrees to get to my final answer I wanted to make sure if I had to do this in degrees or radians. Considering that the answers in the examiner report and marking scheme state values calculated in radians with no explanation as to why. So what's up with that?

    P.S

    The quote tag has not been closed in your post
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  4. #4
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    Hello, unstopabl3!

    1) What I want to know is that since it doesn't state in the question whether to calculate
    the values of the sectors and arc lengths by using the angles in degrees or radians,
    if I calculate my answers with angles in degrees (since in the question an angle, 90,
    is already given in degrees), would my answers be correct/acceptable? . Yes
    Since the answer will be in cm or cm², your angle-units won't matter.

    2) Do we always calculate the values in such sector based questions based upon radians
    or does the examiner define whether to use degrees or radians?
    I would use radians . . . simply because the formulas are simpler.

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  5. #5
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    Thanks for the quick reply.
    So the general formula for finding out the area of a sector " \frac{1}{2}r^2theta " the theta value here is implied by default as to be in radians or degrees? (That is if it is not mentioned in the question what to use radians or degrees). I am unclear about your first statement because if I use an angle 90 degrees in the above formula the answer comes out to be a big one in cm or m but if I use pi/2 radians then the answer won't be as big.
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  6. #6
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    simple sector problem

    Greetings unstopabl3,
    This really is a simple problem. You were asked to give answers in cm or cm^2 and for me I do what I think is the right method without bringing radians into the picture it is apparent that the radius of the circle centered @ A has a radius of 6 x rad 2 and that the full sector and full segment created by drawing arc BD to meet BO extended @F is 1/4 of the 6rad2 circle.
    Answer for arc BD is 1/8 x2 pi x 6rad2 6.66 cm
    Answer for seg BDO 1/4 pi x6rad2^2 - 36 divided by 2 10.27cm^2

    If radian measures simplifly this I'd like to see that solution

    bjh
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  7. #7
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    Hmm, you said "without bringing radians into the picture" and yet you are calculating your values by multiplying by pi ... lol

    pi = radians and you posted your solution by using pi ... so I am confused as to what you are trying to say???
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