MHB Finding X & Y Components of Vectors

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To find the x and y components of a vector, the formulas Ax = A cos(θ) and Ay = A sin(θ) are used. For a vector of 9.55 m at -48.0 degrees, the calculation for Ay results in approximately -7.10 m after applying the sine function. A reminder is given to ensure the calculator is set to the correct mode, as using radians instead of degrees can lead to errors. Additionally, the property of sine is highlighted, noting that sin(-x) equals -sin(x). Understanding these principles is essential for accurately determining vector components.
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Im learning about how to find the x and y components of a vector, but I wanted to verify if I'm on the right track..

Ax=A cos(\theta) <-- solving for x

Ay=A sin(\theta) <-- solving for y

So if a vector is 9.55m long and points in a -48.0 degree direction.

Is it Ay= 9.55 sin(-48.0)=7.3
 
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I get:

$$A_y=9.55\sin\left(-48^{\circ}\right)\text{ m}=-9.55\sin\left(48^{\circ}\right)\text{ m}\approx-7.10\text{ m}$$

Your calculator is in radian mode...and don't forget $\sin(-x)=-\sin(x)$...:D
 
Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?

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