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

- Follow these steps
- 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