Solve the problem.
-Find the tangent to $y = \cos x$ at $x = \frac { \pi } { 2 }$.
A) $y = - x + \frac { \pi } { 2 }$
B) $y = - x - \frac { \pi } { 2 }$
C) $\mathrm { y } = 1$
D) $y = x + \frac { \pi } { 2 }$

Question

Quizplus · Accepted Answer

To find the tangent line to $y = \cos x$ at $x = \frac{\pi}{2}$, we first differentiate $y = \cos x$ to get $y' = -\sin x$. At $x = \frac{\pi}{2}$, $y' = -\sin(\frac{\pi}{2}) = -1$. The value of $y$ at $x = \frac{\pi}{2}$ is $\cos(\frac{\pi}{2}) = 0$. So, the equation of the tangent line is $y - 0 = -1(x - \frac{\pi}{2})$, which simplifies to $y = -x + \frac{\pi}{2}$.

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