1. 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

2. Originally Posted by miley_22
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

3. Originally Posted by miley_22
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

4. Originally Posted by miley_22
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

5. thanks a lot, it really helped!