(a) What is the derivative of $\sin t$ ?
\[
\frac{d}{d t} \sin t=
\]
(b) The velocity of a particle at time $t$ is $v(t)=\cos t$. Use the Fundamental Theorem of Calculus to find the displacement of the particle between $t=0$ and $t=\frac{15 \pi}{2}$.
\[
\int_{0}^{\frac{15 \pi}{2}} \cos t d t=
\]

Answer

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Answer

$\boxed{-1}$

Steps

Step 1 ：$\frac{d}{d t} \sin t = \cos t$

Step 2 ：$\int_{0}^{\frac{15 \pi}{2}} \cos t d t = \sin t \Big|_{0}^{\frac{15 \pi}{2}}$

Step 3 ：$= \sin\left(\frac{15 \pi}{2}\right) - \sin(0)$

Step 4 ：$= -1 - 0$

Step 5 ：$\boxed{-1}$