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Math Help - solving trigonometry questions

  1. #1
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    solving trigonometry questions

    1.
    prove that cosAcos(30-A)cos(30+A)= 1/4 cos3A
    Hence, evaluate cosAcos(30-A)cos(30+A) when A= 170 degree;
    give your answer in exact value.

    2.
    Assuming r is positive, find r and the value of θ between -180degree and 180 degree which satisfy the questions:
    r cos θ= -6 and r sin θ= 1.5
    Give your answer to the nearest minute.
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  2. #2
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    Quote Originally Posted by kelvinchy View Post
    1.
    prove that cosAcos(30-A)cos(30+A)= 1/4 cos3A
    Hence, evaluate cosAcos(30-A)cos(30+A) when A= 170 degree;
    give your answer in exact value.

    2.
    Assuming r is positive, find r and the value of θ between -180degree and 180 degree which satisfy the questions:
    r cos θ= -6 and r sin θ= 1.5
    Give your answer to the nearest minute.
    for#1, you'll need to use the cosine sum/difference identity \cos(x\pm y) = \cos{x}\cos{y} \mp \sin{x}\sin{y} for both the cosine sum and difference factors on the left side ... then simplify. then you'll need to rewrite the right side \cos(3A) as \cos(2A + A) and use the same identity to expand and simplify this expression. bottom line is ... lots of grunt work algebra in front of you.


    for #2, note the polar/cartesian equations below ...

    x = r\cos{\theta}<br />

    y = r\sin{\theta}

    r = \sqrt{x^2+y^2}

    since (x,y) is in quad II , \theta = 180 + \arctan\left(\frac{y}{x}\right)
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