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

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

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

show that the curvature of a circle of radius 'a' equals 1/a
Let $r(t)=a\cos(t)+a\sin(t)$ be a circle of radius $a$.

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

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

Now you do the work.