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Calculator inverse tangent problem

  1. Feb 9, 2007 #1
    1. The problem statement, all variables and given/known data
    Suppose that a wind is blowing from the direction N45ºW at a speed of 50 km/h. A pilot is steering a plane in the direction N60ºE at an airspeed of 250 km/h. Find the true course (direction) and ground speed (magnitude) of the plane.

    2. Relevant equations

    3. The attempt at a solution

    The resultant vector will be in an upward direction in the second quadrant, right? I determined that the resultant vector
    v = <25(√2) - 125(√3), 25(√2) + 125>

    I am trying to find the angle that the plane is flying.
    tan θ = [25(√2) + 125]/[25(√2) - 125(√3)]
    Using inverse tangent and my calculator, I got an angle around -41.5 degrees.
    If the resultant vector is in the second quadrant, this is wrong. I remember that the calculator sometimes will not work for inverse tangent, but I can't remember when, or what to do to fix it.

    Please help.
  2. jcsd
  3. Feb 9, 2007 #2

    D H

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    Staff Emeritus
    Science Advisor

    Use your trig identities. What is [itex]\tan(\theta+180^\circ)[/itex]?
  4. Feb 9, 2007 #3
    The same thing...I was thinking I had to add something. I couldn't remember what though. Thanks
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