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Math Help - [SOLVED] Radians/degrees conversions, want confirmation of answers

  1. #1
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    Question [SOLVED] Radians/degrees conversions, want confirmation of answers

    k well ... i did the following

    1. Convert the angle given in degrees to radian measure in terms of pi.
    380*
    Round the coefficient to two decimal places


    well i converted 380* in terms of pi
    and i got : 19/9 pi ( its wrong)

    2. Evaluate to four significant digits.
    sin^2 pi/3 + cos pi/3

    sin^2 pi/3 + cos pi/3
    and i got : 1.019 ( and this is wrong as well)

    3. A satellite is in a circular orbit 225 km above the equator of the earth. How many kilometres must it travel for its longitude to change by 86.3? Assume the radius of the earth equals 6400 kilometres.
    Round the answer to the whole.


    86.3* x pi/180* = 1.506 rad theta = s / r

    1.506 rad x 225 km = s
    338.89 = s ( rounded to the nearest whole number)
    340 = s ?

    4. Solve the equation 8- tan theta = 0 for all nonnegative values of theta less than 360* . Do by calculator, if needed, and give the answers to three significant digits in the order of increasing.

    inverse tan (8) = angle
    theta = 82.9 (3 sig figs)
    theta = 263 (3 sig figs)
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  2. #2
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    Quote Originally Posted by rock candy View Post
    k well ... i did the following

    1. Convert the angle given in degrees to radian measure in terms of pi.
    380*
    Round the coefficient to two decimal places


    well i converted 380* in terms of pi
    and i got : 19/9 pi ( its wrong)
    No, this is correct. To convert from degree to radian you multiply the theta (in degree) value by \frac{\pi}{180}.

    \therefore 380 \times \frac{\pi}{180} = \frac{19\pi}{9} \approx 6.63 \ {\mathrm{Radians}}

    Quote Originally Posted by rock candy View Post
    2. Evaluate to four significant digits.
    sin^2 pi/3 + cos pi/3

    sin^2 pi/3 + cos pi/3
    and i got : 1.019 ( and this is wrong as well)
    You have an arithmetic error.

    \sin \left(\frac{\pi}{3} \right) = \frac{\sqrt{3}}{2} \therefore \sin ^2 \left(\frac{\pi}{3} \right) = \left(\frac{\sqrt{3}}{2}\right)^2 = \frac34

    \cos \left(\frac{\pi}{3} \right) = \frac12

    Quote Originally Posted by rock candy View Post
    3. A satellite is in a circular orbit 225 km above the equator of the earth. How many kilometres must it travel for its longitude to change by 86.3? Assume the radius of the earth equals 6400 kilometres.
    Round the answer to the whole.


    86.3* x pi/180* = 1.506 rad theta = s / r

    1.506 rad x 225 km = s
    338.89 = s ( rounded to the nearest whole number)
    340 = s ?
    The total distance (radius to be used) is the radius of the earth plus distance to the satelite.

    \therefore r = 6400 + 225 = 6625 \ \mathrm{km}

    Quote Originally Posted by rock candy View Post
    4. Solve the equation 8- tan theta = 0 for all nonnegative values of theta less than 360* . Do by calculator, if needed, and give the answers to three significant digits in the order of increasing.

    inverse tan (8) = angle
    theta = 82.9 (3 sig figs)
    theta = 263 (3 sig figs)
    This is correct.
    Last edited by Jhevon; March 6th 2009 at 05:50 PM. Reason: fixed an error in the answer to problem 2
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  3. #3
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    k i got 1 and 4 right ..

    2 i got wrong .. the answer was this


    answer is 1.25

    3. i added the 2 radius to get the total like you and used theta = s / r ... and i got 9980 km ... :S and its wrong
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by rock candy View Post
    2 i got wrong .. the answer was this


    answer is 1.25
    an error in regards to this problem was made in the previous post, it has been fixed. check again

    3. i added the 2 radius to get the total like you and used theta = s / r ... and i got 9980 km ... :S and its wrong
    you rounded up too much. it should be 9979
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