>Laws of exponents
>Laws of exponents
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*Harmonic functions
*Harmonic function
Functions which are periodic as well as bounded are called harmonic functions
sinθ & cosθ are harmonic.
*Even & odd functions
*Even & odd functions
A function f (x) is called even, if f (- x) = + f (+x).
called, odd, if f (- x) = – f (+x).
otherwise called neither even nor odd.
cos and sec are even and remaining tan, cot, csc & sin are odd, thus
cos(- x) = + cos x & sec(- x) = + secx
sin(- x) = – sin x & csc(- x) = – csc x
tan(- x) = – tan x & cot(- x) = – cot x
*Sin & cos as projections
*Sin & cos as projections
Actually cos & sin gives us an ideas of projections (shadows) of a line on x & y axis respectively. Consider a line of length L making an anticlockwise angle q with + x axis. Let Lx (= ON) &Ly (= OM) be its x & y projections, then
If θ is increased from 00 to 900, then cosθ decreases & sinθ increases.
sin2 θ + cos2 θ = 1
cosec2 θ – cot2 θ = 1
For integral values of n
^A long horizontal fixed wire carries a current of 100 A. Directly above and parallel to it is another wire carrying a current of 20 A and weighing 0.04 N/m.
^A long horizontal fixed wire carries a current of 100 A. Directly above and parallel to it is another wire carrying a current of 20 A and weighing 0.04 N/m. The separation between the two wires so that the upper wire is just supported by the magnetic repulsion is
