The radius of curvature of y = cos x at (?, -1) is

A)1
B) $\frac { 1 } { 2 \sqrt { 2 } }$
C) $\frac { 2 } { 5 \sqrt { 5 } }$
D) $\frac { 2 } { 17 \sqrt { 17 } }$
E) $\frac { 7 } { 125 }$

Question

The radius of curvature of y = cos x at (?, -1) is

A)1
B) $\frac { 1 } { 2 \sqrt { 2 } }$
C) $\frac { 2 } { 5 \sqrt { 5 } }$
D) $\frac { 2 } { 17 \sqrt { 17 } }$
E) $\frac { 7 } { 125 }$

Quizplus · Accepted Answer

The radius of curvature $R$ at any point on a curve is given by $R = \frac { [1 + (y')^2]^{3/2} }{ |y''| }$, where $y'$ and $y''$ are the first and second derivatives of $y$ with respect to $x$, respectively. For $y = \cos x$, $y' = -\sin x$ and $y'' = -\cos x$. At the point $(?, -1)$, $y = -1$ implies $x = \pi$, so $y' = 0$ and $y'' = 1$. Substituting these into the formula gives $R = \frac { [1 + (0)^2]^{3/2} }{ |-1| } = 1$.

The Radius of Curvature of Y = Cos X at 122\frac { 1 } { 2 \sqrt { 2 } }22​1​

The Radius of Curvature of Y = Cos X at $\frac { 1 } { 2 \sqrt { 2 } }$