Let $\,\vec v\,$ be a vector with known magnitude $\,\\vec v\\,$ and known direction.
How can this information be used to find the analytic form, $\,\vec v = \langle a,b\rangle\,,$ of the vector?
In other words, given the magnitude and direction of a vector, what are its horizontal and vertical components?
Trigonometry gives a simple answer,
providing the direction of the vector is specified using the same angle conventions
used to define the trigonometric functions.
For the reader's convenience, these angle conventions are repeated below:



The direction of a vector can be specified in different ways.
A bearing is an acute angle measured
from due north or due south.
Bearings are often used for navigation. For example, the description ‘N $\,60^\circ\,$ W’ means:

N $\,60^\circ\,$ W 
S $\,75^\circ\,$ E 
As you go through the day, Never Eat Soggy Waffles WE, not EW! 
To use the component formulas derived in this section, direction must be specified as an angle from the positive $x$axis (positive up, negative down). Two examples of switching from bearings to standard angles $\,\theta\,$ are given at right. Of course, infinitely many values of $\,\theta\,$ are possible. Only simple choices are shown here. 
N $\,60^\circ\,$ W $\,\theta = 150^\circ\,$ or $\,\theta = 210^\circ\,$ 
S $\,75^\circ\,$ E $\,\theta = 15^\circ\,$ or $\,\theta = 345^\circ\,$ 
Find the analytic representation of the vector $\,\vec v\,$ shown at right. It has length $\,7\,$ and direction indicated. As needed, round to three decimal places. 
As long as you provide the correct component signs (plus/minus) yourself,
then you can use the $\,20^\circ\,$ angle:
On this exercise, you will not key in your answer. However, you can check to see if your answer is correct. 
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