Problem: What are the x and y components of a vector whose length is 24.04 and whose angle with the positive x axis is 44.99 degrees?
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Solution: The x component is 24.04 cos( 44.99 deg) = 17. The y component is 24.04 sin( 44.99 deg) = 17.
Generalized Response: The components of a vector of magnitude v which makes angle `theta with the positive x axis, as measured counterclockwise from the axis, are vx = v cos(`theta) and vy = v sin(`theta). These components can be understood geometrically from a sketch in which the magnitude of the vector its represented by its length, and its angle with respect to a standard set of coordinate axes. The sine and cosine (abbreviated sin and cos as above) are simply the ratios between the y component of the vector and its length, and between the x component and the length.
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Figure description: The figure below depicts a vector of length v making angle `theta with the positive x axis, as measured counterclockwise from that axis. The components vx and vy can be seen as sides of a right triangle formed by the vector and by projection lines parallel to the coordinate axes.
