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Math Help - trig derivatives

  1. #1
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    trig derivatives

    hey, i have a couple of questions!

    1. A triangle has its vertices at A(-1,3), B(3,6), and C(-4,4). Show that, to three significant figures, cosB(angle A)C = -0.569.

    2. The function f is given by f(x) = 2sin(5x-3).
    (a) find f"(x)
    (b) write down f(x)dx

    3. There is a cube, OABCDEFG, wehre the length of each edge is 5 cm. Express the following vectors in terms of i, j, and k.
    (a) vector OG
    b) vector BD
    (c) vector EB

    thats all, thanks
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by miley_22 View Post
    1. A triangle has its vertices at A(-1,3), B(3,6), and C(-4,4). Show that, to three significant figures, cosB(angle A)C = -0.569.
    I am confused at your notation: "cosB(angle A)C"
    What is this? Is it supposed to be the cosine of angle A? (Specifically the cosine of angle BAC?)

    My suggestion is this: Since this isn't a right triangle, my only thought is to use the Law of Cosines which says:
    BC^2 = AB^2 + AC^2 - 2AB \cdot AC \cdot cos(A)

    cos(A) = \frac{AC^2 + AB^2 - BC^2}{2 \cdot AB \cdot AC}

    I get
    cos(A) = -\frac{9 \sqrt{10}}{50} \approx -0.56921

    -Dan
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  3. #3
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by miley_22 View Post
    2. The function f is given by f(x) = 2sin(5x-3).
    (a) find f"(x)
    (b) write down f(x)dx
    a) f(x) = 2sin(5x - 3)

    f^{\prime}(x) = 2cos(5x - 3) \cdot 5 = 10cos(5x - 3)

    f^{\prime \prime}(x) = 10 \cdot -sin(5x - 3) \cdot 5 = -50 sin(5x - 3)

    b) "write down f(x)dx"

    I don't understand what your question is. Are you possibly asking for \int f(x) dx?

    \int 2sin(5x - 3) dx = 2 \int sin(5x - 3) dx

    Let y = 5x - 3 ==> dy = 5 dx

    \int 2sin(5x - 3) dx = 2 \int sin(5x - 3) dx = 2 \cdot \frac{1}{5} \int sin(y) dy = \frac{2}{5} \cdot -cos(y) + C

    So finally:
    \int 2sin(5x - 3) dx = -\frac{2}{5} \cdot cos(5x - 3) + C

    -Dan
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by miley_22 View Post
    3. There is a cube, OABCDEFG, wehre the length of each edge is 5 cm. Express the following vectors in terms of i, j, and k.
    (a) vector OG
    b) vector BD
    (c) vector EB
    We need more information. What are the coordinates of each point of the cube? At least tell us where the x, y, and z axes are in terms of the points on the cube, because the answers depend on this information.

    -Dan
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  5. #5
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    thanks a lot, it really helped!
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