I learned trignometry on the basis of right-angled triangles.Is it applicable to all(acute and obtuse) triangles?and how do you explian cos or sin(<=90),since it's no longer associated with right angled triangle?.can anyone please clarify.
When applied to non-right triangles, the Law Of Sines and Law Of Cosines are used. One way that you can derive these "Laws" is to break the non-right triangle into right triangles and compute the relations among the pieces. Although the definitions of sine and cosine involve only right triangles, they can be applied to more complex situations that can be broken into right triangles.Even after having a look on that link i would say the same, the geometrical meaning of trigonometry is associated with only right triangles.
It is perfectly possible to derive the properties of the sine and cosine functions based on definitions wholly independent of the concdept of "right angles".
For example, they can be regarded as the solutions of a second-order Sturm-Liouville differential equation; the periodicity of the functions is in this case a derivable property, rather than an "axiomatic" property.