Question

If R(t) = cost. Sint. then R(s).R(t)=
-sint. Cost

Answer 1

SOLUTION

Let us differentiate r(t) in terms of t,

So we have,

$\frac{ds}{dt} = 1-2 {\sin}^{2} t$

$\frac{ds}{dt} = 0 \\ = > 1 - 2 {\sin}^{2} t = 0 \\ = > {\sin}^{2} t = \frac{1}{2} \\ = > t = 30$

R(30)=\cos30\sin30=1/2 × root3/2

$= \frac{ \sqrt{3} }{4}$

$r(s).r(t) = - \sin(t)\cos(t) \\ = > r(s). \frac{ \sqrt{3} }{4} = -\sin30 \cos30 \\ = > r(s) = - 1$