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Well!why do we consider only direction cosines and not direction sines or tans. What is its actual significance?and how to use them?

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Good question. According to the definition, direction cosines give the cosines of the angles which the vector makes with the positive $x,y,z$ axes. The angles range between $0$ and $180$ degrees and they give a unique direction of the vector.

If you see, $\cos x$ is continuous and takes distinct values in $[0,\pi]$ and that's what distinguishes it from $\sin$ and $\tan$.

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Bcoz, when we consider either sines or tans unlike coses, we involve opposite side which depends on the plane we consider in measuring alpha, beta and gamma.

For eg: We can measure alpha in either XY or XZ plane(a plane containing X as one of its axis).

So, sin(alpha) in XY =b/a;

sin(alpha) in XZ =c/a

So involving opposite side does not give a unique line.

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    $\begingroup$ Please, typset mathematical expressions using MathJax. $\endgroup$ – mucciolo Nov 19 '17 at 5:37

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