Click on a sign to toggle it. The vector is written (x,y).
Click on a trig function to swap it with the other one.
Click on "OK" when you think your expression matches the vector.
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\(\def\rect{\sqsubset\!\sqsupset}\)
All vectors can be written in the form $$\vec v = \pm|v|\rect\theta \pm |v|\rect\theta,$$ where one \(\rect\) is replaced with "sin" and one with "cos". The axis (x or y) that the angle is measured from gets the cosine.
For example, this vector \(\vec v\) can be written
$$\vec v = ({\color{red} -}|v|{\color{blue}\cos}\ 60^\circ, {\color{red}-}|v|{\color{blue}\sin}\ 60^\circ)$$
because
The 60° angle is measured from the x axis, so the cosine goes in the x component, while the y component gets the sign.
The arrow points in a leftward direction, so the x component is negative (in this basis).
The arrow points in a downward direction, so the y component is also negative.