LearninDaMath
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Homework Statement
Find y component of vector C from its length and the angle it makes with the x axis, that is, from geometry. Express the y component of vector C in terms of C and \phi.
Homework Equations
Vector addition using geometry:
1) C = \sqrt{A^{2}+B^{2}-2ABcos(c)}. Law of Cosines
2) \phi = sin^{-1}\frac{Bsin(c)}{C}. Law of Sines
Vector addition using components:
3) C_{x} = A + Bcos\vartheta.
4) C_{y} = Bsin\vartheta
The Attempt at a Solution
Since I'm supposed to use geometry, I'm limited to using equations 1 or 2 (Law of cosine and sin)
I could easily determine C_{y} by making a right triangle and forming the equation: [sin\phi=\frac{Cy}{C}] = C_{y} = Csin\phi
However, that would be using the component addition method. I don't see how I would use geometry (Law of sine or cosine) to produce the same answer of Csin\phi.
The only thing I could come up with was taking SAS (side angle side) \sqrt{C}_{y}^{2} = \sqrt{C^{2}+C_{x}^{2}-2C_{x}Ccos\phi} , but then how does that equate to
C_{y} = Csin\phi ?
Am I supposed to find the side using the Law of Cosine equation? If so, then
Have I described the correct way of proceeding with the problem? If so, then
Did I come up with the correct Law of Cosine forumula? If so, then
Am I supposed to put it in the same form that I would have gotten using component addition? ( C_{y} = Csin\phi) ? If so, then
How does \sqrt{C^{2}+C_{x}^{2}-2C_{x}Ccos\phi} turn into Csin\phi if they are essentially equal to each other and represent C_{y}?
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