Trigonometric functions - I
There are six basic trigonometric functions.
1. sin x
2. cos x
3. tan x
4. cosec x
5. sec x
6. cot x
To draw the graph of these functions we will consider a circle of unit radius and observe the behaviour of these trigonometrical function as point P moves anticlockwise in the below figure.
1. f(x) = sinx
since, sin x = a
Observe the variations in 'a' in the above figure
From above figure, it can be concluded that
when x = 0, sin x = 0
when
, sin x = 1
and after every interval of
, the 'sin x' repeats its values
i.e. f(x) = sin x is a "periodic function" of period ![2\pi](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_vsnYZ34k6VkbsevDNZiq16m_BKQObAXrh5OYrIw4MPdd52sAWkolDrTrP9d5S9bBPJesY_7GZLwbuItQXMVv_sFmm6E-0DeiJsUE4mLFk9oyrrPCOoi9RM5Wgs0uBq0KkwW8KH8pTIIo8ARI4lBktQMLDLh_akZLMvGVcHikA=s0-d)
observe the variation of 'a', the graph of 'sin x' is given below
Domain = R
Range = [-1,1]
2. f(x) = cos x
since, cos x = b
observe the variation of 'b'
i.e. f(x) = cos x is a "periodic function" of period ![2\pi](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_vsnYZ34k6VkbsevDNZiq16m_BKQObAXrh5OYrIw4MPdd52sAWkolDrTrP9d5S9bBPJesY_7GZLwbuItQXMVv_sFmm6E-0DeiJsUE4mLFk9oyrrPCOoi9RM5Wgs0uBq0KkwW8KH8pTIIo8ARI4lBktQMLDLh_akZLMvGVcHikA=s0-d)
Domain = R
Range = [-1,1]
3. f(x) = tan x
since tan x = a/b
observe the variation in 'a/b'
Range = R
It repeats its value after every interval of ![\pi](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_vl5aUm-W68meTDr_71kmc51ajAj9SHVkOWJW0L8gjEvj1_j8_m3qrOD3gnMMwsSvQQ2uUnyW-58vZ5IKreVMQ5TK6JVTkQSTZT1tVO9nRv-snpZOHsEWmScmHcIkHNaYcGLkIVb4eq8pY53VGz5RDG7GenAEjtHa9JtIySgw=s0-d)
i.e. f(x) = tan x is a "periodic function" of period ![\pi](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_vl5aUm-W68meTDr_71kmc51ajAj9SHVkOWJW0L8gjEvj1_j8_m3qrOD3gnMMwsSvQQ2uUnyW-58vZ5IKreVMQ5TK6JVTkQSTZT1tVO9nRv-snpZOHsEWmScmHcIkHNaYcGLkIVb4eq8pY53VGz5RDG7GenAEjtHa9JtIySgw=s0-d)
sir,
ReplyDeleteplease upload trigonometry quetions for ssc CGL main exam 2013
thanks
This blog is for IIT aspirants. For CGL main exam, i will post trigonometry after some time on shiksha4all page
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ReplyDeleteA clock gains 5 minutes every hour. The angle traversed by the second hand in one minute is ??