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Math Help - Trig Brain Cramp

  1. #1
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    Trig Brain Cramp

    The problem says:

    An airplane is flying on a horizontal path at a height of 3800 ft. At what rate is the distance s between the airplane and a fixed point P (on the ground) changing with respect to theta when theta equals 30 degrees? Express your answer in units of ft/degree.

    I understand the problem, and got -13,163.2 feet/??? Here is my dilemma:

    The answer key says that this answer is in ft/rad and that I need to convert it to ft/deg, which is approximately -230 ft/deg. My question: WHY? If I plug 30 DEGREES into my calculator and get -13,163.2 feet, isn't that in DEGREES? I know HOW to do the conversion. I am not clear on why. Help?

    Jeannine
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  2. #2
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    The answer key says that this answer is in ft/rad and that I need to convert it to ft/deg, which is approximately -230 ft/deg. My question: WHY? If I plug 30 DEGREES into my calculator and get -13,163.2 feet, isn't that in DEGREES? I know HOW to do the conversion. I am not clear on why. Help?
    because the derivatives of the trig functions you have learned are only valid when \theta is in radians ... substituting in 30 degrees at the end of the problem using degree mode in your calculator only gave a specific value of the trig ratio in your expression that determined the desired rate of change, you would have gotten the same result substituting in \frac{\pi}{6} in radian mode.
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