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Nilanjan Bhowmick AIR 3, CSIR NET (Earth Science)
- IIT JAM
- Physics (PH)
Physics basic doubt
why always component with angle is taken as cos@ and component other than angle is taken as sin@?, like in this fig also. Is there any mathematical proof for this??
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Ruby negi
u know trigonometric formulas, cos@ is base/hypotenuse that's why base( side that makes angle with hypotenuse) is cos@*hypotenuse (in this case it is Rcos@).. similarly sin@=perpendicular/hypotenuse
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Dhairya sharma
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it's an mathamatical conversation. cosa shows projection on the base . and comes here from maths like
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Shanu arora
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actully it comes from the defination of cos@= base / hypotenuse and sin@ = perpendicular / hypotenuse , so see this purely mathematical .
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Abhishek singh
The mathematics behind your doubt is discussed well. I would like to give you some intutions based on my views. Assume a right triangle(a triangle with one angle 90°), if you increase any one side of the right triangle taking the angle constant, you have to increase all the sides in proportion to make the angle constant otherwise you will end up changing the angles too(try to imaging this, if you are not able to imagine, draw this on paper and try.) increasing one side results in increment in other two sides. triangle have three sodes, so you can have 3! (factorial, 3! = 3*2*1 = 6) combinations of proportions. And these all six proportion are named six trigonometric functions. they are just names, which are fixed by great mathematicians and we are following this name conventions(the mathematician who discovered this has give name "sine@" to the proportionality between perpendicular and hypotenuse for a given angle and similarly rest of all 5 trigonometric functions) This will help you in having all possible approach of thinking about a simple thing. Regards.