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Thread: VCE Maths questions help

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    Re: VCE Maths questions help

    evaluate tan (2pi/3)
    = (3pi/3) - (pi/3)
    =(pi) - (pi/3)
    =+ tan (pi/3) = (√3)
    Is this correct?
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    Re: VCE Maths questions help

    why is cos (-pi/4) the same as cos (pi/4)?
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    Re: VCE Maths questions help

    Quote Originally Posted by boredsatan View Post
    evaluate tan (2pi/3)
    = (3pi/3) - (pi/3)
    =(pi) - (pi/3)
    =+ tan (pi/3) = (√3)
    Is this correct?
    Not sure what you've done in the second line, but that seems unnecessary for that question anyway. Using angles of any magnitude, you know tan(2pi/3) is in the second quadrant, which is negative for tan.

    So tan(2pi/3) = -tan(pi/3) = -√3
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    Re: VCE Maths questions help

    Quote Originally Posted by Sp3ctre View Post
    Not sure what you've done in the second line, but that seems unnecessary for that question anyway. Using angles of any magnitude, you know tan(2pi/3) is in the second quadrant, which is negative for tan.

    So tan(2pi/3) = -tan(pi/3) = -√3
    Thanks!
    also, do you know why is cos (-pi/4) the same as cos (pi/4)?
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    Re: VCE Maths questions help

    The first four quadrants are positive for cos. (pi/4) is obviously in the first quadrant, and if you can see that (-pi/4) is actually in the fourth quadrant, then both cos(pi/4) and cos(-pi/4) are positive (1/√2). It might not be the best explanation because this is much easier to show with a diagram of the quadrants, but I hope it helps anyway.
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    Re: VCE Maths questions help

    If pr(A) = 0.45, pr(B) = 0.35, and pr(A inverted u B) = 0.25, how would you find Pr (A' inverted u B')
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    Re: VCE Maths questions help

    convert 7pi/12 to degrees
    (7pi/12)*(180/pi)
    =1260pi/12pi
    = 105
    is this correct?
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    Re: VCE Maths questions help

    Quote Originally Posted by boredsatan View Post
    convert 7pi/12 to degrees
    (7pi/12)*(180/pi)
    =1260pi/12pi
    = 105
    is this correct?
    anyone?
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    Re: VCE Maths questions help

    Anyone know how to work out tan (5pi/4) as i'm really confused?
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    Re: VCE Maths questions help

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    Re: VCE Maths questions help

    Quote Originally Posted by boredsatan View Post
    Anyone know how to work out tan (5pi/4) as i'm really confused?
    yeah the exact value is sqrt(6Pi/9)
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    Re: VCE Maths questions help

    Quote Originally Posted by boredsatan View Post
    Anyone know how to work out tan (5pi/4) as i'm really confused?
    tan(5pi/4) = tan(pi/4 + pi)
    = (tanpi + tan(pi/4))/(1-tanpi*tan(pi/4))
    = (0+1)/(1-0)
    = 1
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    Re: VCE Maths questions help

    Quote Originally Posted by pikachu975 View Post
    tan(5pi/4) = tan(pi/4 + pi)
    = (tanpi + tan(pi/4))/(1-tanpi*tan(pi/4))
    = (0+1)/(1-0)
    = 1
    pikachu: more directly this way:

    tan(pi/4 + pi) = tan(pi/4) = 1
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    Re: VCE Maths questions help

    How would you work out tan (-2pi/3)
    I'm confused as it's negative
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    Re: VCE Maths questions help

    Quote Originally Posted by boredsatan View Post
    How would you work out tan (-2pi/3)
    I'm confused as it's negative
    It's in the 3rd quadrant so it's positive since tan is positive in the third quadrant.

    tan(pi/3) = tan(-2pi/3) = sqrt3
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    Re: VCE Maths questions help

    in a population of 10,000 people, 75% spoke german, 45% spoke french, and 10% of the population did not speak either french or german
    draw a venn diagram
    how do you work out how many people speak both french and german, given that it's not stated above?
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    Re: VCE Maths questions help

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    Re: VCE Maths questions help

    solve cos(x) = 0.5, (-4pi to 4pi)
    base = pi/3,
    +ve rotation
    x = pi/3, 2pi-pi/3 = 5pi/3
    pi/3 + 2pi = 7pi/3
    5pi/3 + 2pi = 11pi/3

    -ve rotation
    x = -pi/3, x = -2pi + pi/3 = -5pi/3
    -2pi - (-pi/3) = -5pi/3
    -2pi - (-5pi/3) = -pi/3

    are these answers right?
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    Re: VCE Maths questions help

    Quote Originally Posted by boredsatan View Post
    solve cos(x) = 0.5, (-4pi to 4pi)
    base = pi/3,
    +ve rotation
    x = pi/3, 2pi-pi/3 = 5pi/3
    pi/3 + 2pi = 7pi/3
    5pi/3 + 2pi = 11pi/3

    -ve rotation
    x = -pi/3, x = -2pi + pi/3 = -5pi/3
    -2pi - (-pi/3) = -5pi/3
    -2pi - (-5pi/3) = -pi/3

    are these answers right?
    cos(x) is an even function so cos(x) = cos(-x). If you have 7pi/3 and 11pi/3, you must also have -7pi/3 and -11pi/3.

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    Re: VCE Maths questions help

    Quote Originally Posted by boredsatan View Post
    in a population of 10,000 people, 75% spoke german, 45% spoke french, and 10% of the population did not speak either french or german
    draw a venn diagram
    how do you work out how many people speak both french and german, given that it's not stated above?
    10,000 people
    7,500 German
    4,500 French
    1,000 Neither

    If N people speak both,
    (7500 - N) + (4500 - N) + N + 1000 = 10000
    N = 3000 people

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