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Inverse Trig Function Problem

  1. Nov 21, 2013 #1
    1. The problem statement, all variables and given/known data
    A patrol car is 50 ft from a long warehouse. The revolving light on top of the car turns at a rate of 30 rotations per minute. How fast is the beam of light moving along the warehouse wall when the beam makes a 45° angle with the line perpendicular from the light to the wall?


    2. Relevant equations



    3. The attempt at a solution
    First I started out by setting θ as a function of x : tanθ=(x/50)→θ=arctan(x/50). So when θ=45°, x=50ft. dθ/dt is 30(2∏)=60∏. So taking the derivative: dθ/dt=[(50)/(502+x2)]dx/dt. After substituting values, 60∏=(0.01)dx/dt→dx/dt=6000∏ ft/min. Is this right?
     
  2. jcsd
  3. Nov 21, 2013 #2

    Dick

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    Yes, it is right. But you didn't really need to go through the arctan stuff. Just differentiate both sides of 50tanθ=x.
     
    Last edited: Nov 21, 2013
  4. Nov 21, 2013 #3
    Okay, thank you. The reason that I did the arctan stuff was because we're doing arctan derivatives, so I figured my teacher would want me to do it that way.
     
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