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Math Help - Trig Equations

  1. #1
    Junior Member
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    Trig Equations

    Hello. This is a little urgent so hopefully, I'll be able to get answers quickly. I know this may seem rather basic but I'm having some trouble with these two equations. Well, for one of them, I seemed to be able to get most of the answers but one. Could you please answer these in EXACT form and also in radians?

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    First one: (The one I'm struggling with)

    2sinx - cosx = 0

    All I need for this equation is a starting point or working angle(s) and I should be able to finish off the rest.

    -----

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    Second one: (Just wanted to ask a little question)

    sin3x = 0

    For -pi ≤ x ≤ 0

    My working angle is obviously 0.

    That means x = 0 + (2/3)*k*pi where k is an integer

    Now for my answers, I got 0 and -2pi / 3. However, with my calculator, there seems to be another solution which is -pi / 3.

    Now, I was wondering, what value of k would allow me to get that missing answer?

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    Thankyou. All help is of course, appreciated as usual.
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  2. #2
    Senior Member
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    Quote Originally Posted by sqleung View Post
    2sinx - cosx = 0
    A hint:divide by cos(x)

    Quote Originally Posted by sqleung View Post
    sin3x = 0 For -pi ≤ x ≤ 0
    In general you need to remember that if sin(x)=a then sin(pi-x)=a too.

    So for your equation

    3x=2kpi and pi-3x=2kpi

    leading to

    x=2kpi/3 and x=(pi-2kpi)/3
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