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Math Help - trigonometry

  1. #1
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    Post trigonometry

    Give an example, with justification:
    A real life situation requiring the use of a trigonometry identity.








    Knowledge is life, so open your doors of perception.
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  2. #2
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    Anything you want square. Measuring the sides will not get you there unless:

    1) You can verify the corners are right angles, or

    2) You can calculate and measure the diagonals.
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  3. #3
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    Here is one use of identities that is introduced to students in a high school physics class ... the derivation of the range formula for the horizontal displacement of a projectile (Galilean model).

    start with the physics equation for vertical displacement ...

    \Delta y = v_0 \sin(\theta) t - \frac{1}{2}gt^2

    since the projectile lands at the same height it started,
    \Delta y = 0 ...

    0 = v_0 \sin(\theta) t - \frac{1}{2}gt^2

    solving for t ...

    t = \frac{2v_0 \sin(\theta)}{g}

    horizontal displacement is given by the formula ...

    \Delta x = v_0 \cos(\theta) t

    using the last two equations, eliminate the parameter t ...

    \Delta x = \frac{2v_0^2 \sin(\theta) \cos(\theta)}{g}

    using the double angle identity
    \sin(2\theta) = 2\sin(\theta)\cos(\theta),
    the last equation becomes ...

    \Delta x = \frac{v_0^2 \sin(2\theta)}{g}

    from this equation, it can be deduced that the launch angle for maximum horizontal range is 45 degrees.
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