Resolving a vector into components is actually using the vector as the hypotenuse of a triangle and the components as the legs of a right triangle, then finding the legs of the triangle using the definitions of sine and cosine. If the components are to be parallel to the axes, it is often easiest to move the vector temporarily so that its initial point (tail) is at the origin and its direction is preserved. Then the x- and y-components are the x- and y-coordinates of its terminal point (head).

Example 1: Resolve the vector representing the flight of a plane at 200 miles per hour at a heading of 300 degrees into its x- and y-components.

We must remember to include the appropriate signs for x and y because we are using the reference angle of 30° rather than the standard position angle, which is 150°.

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Example 2: Resolve a wind of 40 miles per hour from a heading of 64° into x- and y-components.

We move the vector in the first quadrant with a heading from 64° so that its initial point is at the origin; the vector then is in the third quadrant. As before, we must remember to include the appropriate signs for x and y because we are using reference angles.
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Example 3: Find the actual direction of travel and ground speed of a plane flying at 200 miles per hour at a heading of 300 degrees if there is a wind of 40 miles per hour blowing from a heading of 64°.

We already have the components of the separate vectors, so we can add them (by adding corresponding components).

The ground speed of the plane is 224.8 mph at an actual heading of 291.5°.

This method avoids having to draw the parallelogram and the resultant vector, then calculate one of the angles in the triangle formed by the original vectors and the resultant, then use the law of cosines and law of sines. The price is having to resolve the given vectors into components and, at the end of the problem, find the magnitude and direction of the sum which is written in component form. Either method can be used, depending on one's preference.