I keep getting “Resolving a vector into components” questions wrong in Motion in a Plane. What's the trap?
writing both components positive even when the arrow points left or downward.
The usual trap: writing both components positive even when the arrow points left or downward. How to avoid it: draw the arrow first; cosine sits beside the marked angle, sine sits opposite it, then assign signs. Go back to the definition — A vector is one arrow, but we may replace it by perpendicular x- and y-parts that together produce exactly the same effect. If the vector A makes angle theta with +x, then A_x = A cos(theta) and A_y = A sin(theta); signs come from the actual directions, not from the formula.
Key point
Resolving a vector into components
Common mistake
writing both components positive even when the arrow points left or downward.
Memory tip
draw the arrow first; cosine sits beside the marked angle, sine sits opposite it, then assign signs.
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