## anonymous 4 years ago consider the circle r(t)= (a cos t, a sin t), for 0≤ t ≤ 2pi, where a is a positive real number, compute r' and show that it is orthogonal to r for all t.

1. anonymous

$r(t)= (a\cos t, a\sin t)$$r'(t)= (-a\sin t, a\cos t)$$r(t)\cdot r'(t)=-a^2\sin t\cos t+a^2\sin t\cos t=0$

2. anonymous

does the third step show that its orthogonal?

3. anonymous

$\hat{u}\cdot\hat{v}=|\hat{u}||\hat{v}|\cos\angle{(\hat{u},\hat{v})}=0\quad\Rightarrow\quad\hat{u}\perp\hat{v}$

4. anonymous

yea thats what i was thinking since it has to be right triangle to be orhoganol

5. anonymous

thanks