Answer
$R_{n}(x)=\dfrac{\sin^{(n+1)}(c)x^{n+1}}{(n+1)!}$
Work Step by Step
The Remainder Theorem for some points $c$ and $a$ can be expressed as:
$R_{n}(x)=\dfrac{f^{n+1}(c)(x-a)^{n+1}}{(n+1)!}~~~~~(1)$
We are given the functions $f(x)=\sin x$ and $a=0$
Put these values in the equation (1) to obtain:
$R_{n}(x)=\dfrac{\sin^{n+1}(c)(x-0)^{n+1}}{(n+1)!}$
Thus, we have: $R_{n}(x)=\dfrac{\sin^{(n+1)}(c)x^{n+1}}{(n+1)!}$
