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Math Help - Using a Graphing calculator to verify Trig Eqautions in radian mode

  1. #1
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    Using a Graphing calculator to verify Trig Eqautions in radian mode

    Okay so in one of my previous posts I had to solve Trig. Equations between [0,2PI), to get all solutions and giving exact answers. Another part to the assignment was to check the answers for each radian measure on my calculator and then graph it. I know to check each function you have to plug in the equation and then use the TABLE setting to compare answers, I'm just a bit confused on the graphing aspect of it.

    Here is one of my problems with its solutions in exact answers:


    Problem : 5 Sin ^ 2 x - 8 sin x = -3

    The answer for the left side is 3 / 5 with no radian solution

    The answer for the right is Sin x = 1 and -1

    Its radian mesaures are: PI/2 and 3PI/2
    Last edited by MajorJohnson; April 20th 2011 at 01:57 AM.
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    You can solve this as a quadratic equation, let X = sin(x) to turn the equation into

    5X^2 - 8X = -3

    5X^2 - 8X + 3 = 0

    5X^2 - 5X - 3X + 3 = 0

    5X(X - 1) - 3(X - 1) = 0

    (X - 1)(5X - 3) = 0

    X - 1 = 0 or 5X - 3 = 0

    X = 1 or X = 3/5

    sin(x) = 1 or sin(x) = 3/5.

    Both of these equations will have solutions, it's just you won't be able to get an EXACT answer for sin(x) = 3/5...

    For sin(x) = 1, the only acceptable solution is pi/2.
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    Yes but to solve for all solutions, 3PI/2 would also be a solution, because a -1 is in quadrant 3 right?
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    Quote Originally Posted by MajorJohnson View Post
    Yes but to solve for all solutions, 3PI/2 would also be a solution, because a -1 is in quadrant 3 right?
    Where has 3pi/2 come from? Your explanation does not make sense (and is also wrong since 3pi/2 is NOT a solution - a simple substitution into the original equation clearly shows).
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    Quote Originally Posted by MajorJohnson View Post
    Yes but to solve for all solutions, 3PI/2 would also be a solution, because a -1 is in quadrant 3 right?
    As I have shown, sin(x) does NOT ever equal -1.
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