# Vector Addition And Trigonometry

Vectors can be described as directed segments and as ordered pairs.  However, since it is easier to add vectors as ordered pairs, you would want to translate the vectors from directed segments to ordered pairs. Translation from directed segments to ordered pairs can be done by using trigonometry.

* In a right triangle ABC with right angle C,
the tangent of angle A, written tan(A), is leg opposite angle A divided by (/) leg adjacent to angle A;
the sine of angle A, written sin(A), is leg opposite angle A / hypotenuse;
the cosine of angle A, written cos(A), is leg adjacent to angle A / hypotenuse.

Here is an example:

Describe the vector OD above with an ordered pair.

The desired ordered pair contains the coordinates of point D. Let D = (x,y). From the graph you can see that x is positive and y is negative. The absolute values of x and y are OC and CD. Now use trigonometry.

OC/OD = cos(30°)
OC = OD*cos(30°)
OC = 25*cos(30°)

CD/OD = sin(30°)
CD = OD*sin(30°)
CD = 25*sin(30°)

A = (25*cos(30°), -25*sin(30°) = about (21.65, -12.5)

## Great! Let me try some problems myself!

1. Find the components of the vector whose magnitude is 150 and whose direction is 10 degrees south of west.