# Vectors as Order Pairs

### How to express a vector as an ordered pais

• Align the 'tail' of the vector with the origin
• Determine the x and y coordinates where the head or 'pointy end' of the vector lands. Typically, for this you need to use sine and cosine ratios.

In the picture below, the vector has a magnitude of 60 and its direction is 73° above the positive x axis.

Express the vector below as ordered pairs.

### Practice Problem

x coordinate
$$= 2 \cdot { \bf cos}(30^{\circ}) \\ = 2 \cdot \frac{\sqrt{3}}{2}= \sqrt{3}$$

y coordinate
$$= 2 \cdot { \bf sin}(30^{\circ}) \\ = 2 \cdot \frac{1}{2}=2$$

Ordered Pair: $$( \sqrt{3} , 2 )$$

This was kind of a trick question in that you must recognize that the 60° angle is the same as the prior problem's angle.

x coordinate = 2 ×sin(60°) =

y coordinate = 2 ×cos(60°) = 2(½) = 1

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