show that the curvature of a circle of radius 'a' equals 1/a

[waseemshahzada]

show that the curvature of a circle of radius 'a' equals 1/a
plz help me if any body can solve it plz

 

[pka]

show that the curvature of a circle of radius 'a' equals 1/a

Let \(\displaystyle r(t)=a\cos(t)+a\sin(t)\) be a circle of radius \(\displaystyle a\).

Then \(\displaystyle \bf{T}(t)=\dfrac{r'(t)}{\|r'(t)\|}\).

Then curvature is \(\displaystyle \kappa(t)=\dfrac{\|\bf{T}'(t)\|}{\|r'(t)\|}\).

Now you do the work.