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Math Help - some trignometry simplification

  1. #1
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    Exclamation some trignometry simplification

    Solve the following equations if 0<x<2pie (those are 'less than or equal to') answer to 2 decimal places.

    a) square root of 2 cos(x = pie/2) + 1 = 0


    b) sin(1/2)(x-2pie/9) = 0.6

    i would be greatful to get step by step answers please
    Tom
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  2. #2
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    I'd love to help but have problems understanding things on both questions.

    For a) , what does 2cos(x = pi/2) mean? Is that supposed to be a minus sign?

    For b) , is that supposed to be the sine of one half time the next expression, kind of like (sin .5) times (x-[2pi]/p)?
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  3. #3
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    sorry

    for a) square root of 2 cos(x + pi/2) + 1 = 0

    for b) yes it is the sine of one half time the next expression, kind of like (sin .5) times (x-[2pi]/9) = 0.6
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  4. #4
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    Also, for A, does the square root apply to the whole left hand side or only part of it. Use those parantheses!

    B) I don't have a good calculator handy, so I'll just solve in terms of what you wrote and you can make it into a decimal answer. This is really just like any algebra problem you've gotten before. Isolate x.

    sin(1/2) * (x-[2pi]/9) = .6

    x-[2pi]/9 = (.6/sin[1/2])

    x = (.6/sin[1/2]) + [2pi]9

    From here, it's just making sure you can enter it properly into your calculator to get the right decimal approximation.
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  5. #5
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    for a) square root ONLY applies to the 2 at the front
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  6. #6
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    This could be done using a inverse trig method, but a much easier and in my opinion a much more elegant way uses a common but wonderful observation.

    How are sine and cosine directly related? Well here's an identity that will prove useful.

    cos(a) = sin(pi/2 - a)

    So our problem is:

    sqrt{2}cos(x+pi/2) + 1 = 0

    Now, for this case the "a" is the whole expression "x+pi/2". So we can rewrite this as...

    sqrt{2}sin(pi/2-a) + 1 = 0

    And plugging back in our a...

    sqrt{2}sin(pi/2 - [x+pi/2]) + 1 = 0

    Simplify...

    sqrt{2}sin(-x) + 1 = 0

    sin(-x) = -1 / sqrt{2} or -sqrt{2}/2

    From here you can use your calculator, but it's not necessary. This is a nice angle to work with.
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