what is the actual use of direction cosines... and wht happens actually when we consider direction cosines..please answer in detail..!

## well why do we only consider direction cosines... why not direction sines,tans..??

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# 1 Answer

We are going to describe the direction of a line through the origin. I need to tell you how, starting at the origin, you walk so many steps parallel to the x-axis, then so many steps parallel to the y-axis, then so many steps parallel to the z-axis, to
arrive at a point on the line distant exactly one from the origin. If I stood at that point and dropped a perpendicular on each of the axes in turn, the perpendicular would hit the axis at the point with coordinates (cosΘ

_{x},0,0), (0,cosΘ_{y},0),(0,0,cosΘ_{z}). I need to say that Θ_{x}is the angle between the line and the x-axis, and similarly for the other angles.If you need to walk on a line which doesn't go through the origin, then the same exercise is applied by walking from any point on the line, say (a,b,c), and the answers change to (a+cosΘ

_{x},b,c),(a,b+cosΘ_{y},c),(a,b,c+cosΘ_{z}) which is seen by drawing a set of axes through (a,b,c) rather than the origin.