Why tan theta becomes theta when theta is small?
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as tan0°=0 so tan theta becomes theta when theta is small.
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Hiiii.....
The small-angle approximation is a useful simplification of the basic trigonometric functions which is approximately true in the limit where the angle approaches zero. They are truncations of the Taylor series for the basic trigonometric functions to a second-order approximation. This truncation gives:
{\displaystyle {\begin{aligned}\sin \theta &\approx \theta \\\cos \theta &\approx 1-{\frac {\theta ^{2}}{2}}\\\tan \theta &\approx \theta ,\end{aligned}}}
where θ is the angle in radians.
The small angle approximation is useful in many areas of engineering and physics, including mechanics, electromagnetics, optics(where it forms the basis of the paraxial approximation), cartography, astronomy, computer science, and so on.
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The small-angle approximation is a useful simplification of the basic trigonometric functions which is approximately true in the limit where the angle approaches zero. They are truncations of the Taylor series for the basic trigonometric functions to a second-order approximation. This truncation gives:
{\displaystyle {\begin{aligned}\sin \theta &\approx \theta \\\cos \theta &\approx 1-{\frac {\theta ^{2}}{2}}\\\tan \theta &\approx \theta ,\end{aligned}}}
where θ is the angle in radians.
The small angle approximation is useful in many areas of engineering and physics, including mechanics, electromagnetics, optics(where it forms the basis of the paraxial approximation), cartography, astronomy, computer science, and so on.
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