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Math Help - Trigonometry word problems?

  1. #1
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    Trigonometry word problems?

    1.Circumference of earth is 25,000 mi. At an altitude of 35,000 ft. directly from the NP to a point on the equator, what is the distance traveled?
    Last edited by SoConfused123; November 11th 2012 at 04:43 PM.
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    Re: Trigonometry word problems?

    (1) arclength ... s = r\cdot \theta , where \theta is in radians

    how many radians in a quarter circle?

    (2) I believe the formula , A_x = x\tan \left(\frac{180}{x} \right) is for a circle inscribed in a polygon of x sides.

    A(6) = 3.464...

    A(10) = 3.249...

    A(100) = 3.1426...

    A(1000) = 3.1416...

    A(10000) = 3.14159...

    so ... what value is this approaching?

    (3) yes, 30 ft = distance from crest to trough ...double the amplitude.
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    Re: Trigonometry word problems?

    1. There's pi/2 radians in quarter of a circle?

    2.So it would be approaching pi?
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    Re: Trigonometry word problems?

    Quote Originally Posted by SoConfused123 View Post
    1. There's pi/2 radians in quarter of a circle?

    why the question mark? you should know this ...

    2.So it would be approaching pi?

    sure looks that way ... do you understand what's happening here in a geometrical sense?
    ...
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    Re: Trigonometry word problems?

    1. I know, I should.
    So S= r * pi/2

    So since I have the circumference of the earth being approx. 25,000 mi. would I do 25,000/pi/2= 3978.87 as the radius
    and do 3978.87*pi/2 = 6,250 miles as distance traveled?
    Or am I way off?

    2.I think so.
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    Re: Trigonometry word problems?

    (1) radius of the earth, R_e = \frac{25000}{2\pi}

    the pilot's radius is R_p =  R_e + 35000 \, ft = \frac{25000}{2\pi} + \frac{35000}{5280}

    d = R_p \cdot \frac{\pi}{2}

    (2) as the polygon gets more and more sides, it starts to look like a circle ... what's the area of a unit circle?
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    Re: Trigonometry word problems?

    1. So around 61,695 miles would be the distance traveled. Is that right?

    2. A= pi * r2
    So pi*12= pi
    A= pi
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    Re: Trigonometry word problems?

    Quote Originally Posted by SoConfused123 View Post
    1. So around 61,695 miles would be the distance traveled. Is that right?
    check it again ... how can traveling about 1/4 of the earth's circumference be greater than the earth's circumference?
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    Re: Trigonometry word problems?

    Ah, true.
    I typed it in as radians the first time.

    This time I typed it in as degrees
    69.44+6.62=76.06 * 90 = 6,845 miles

    Is that correct now?
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    Re: Trigonometry word problems?

    \left(\frac{25000}{2\pi} + \frac{35000}{5280}\right) \cdot \frac{\pi}{2} = 6260 \, miles
    Thanks from SoConfused123
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    Re: Trigonometry word problems?

    Blaghfgdgf.
    I typed it in just like you showed it and it still won't come out to your answer.
    Well thank you so much for your help, I'll keep working on it.
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    Re: Trigonometry word problems?

    Quote Originally Posted by SoConfused123 View Post
    Blaghfgdgf.
    I typed it in just like you showed it and it still won't come out to your answer.
    Well thank you so much for your help, I'll keep working on it.
    put the (2\pi) in parenthesis ...
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    Re: Trigonometry word problems?

    Ahh, got it.
    Thanks.
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