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\problemgrouptitle{Trigonometric Limits}

\begin{problemblock}[2]{Evaluate the trigonometric limits.}

\addtoanswerkey{\begin{multicols}{4}}

\item $\displaystyle\lim_{\theta\to0}\frac{\theta}{\sin \theta}$
\answer{$1$}

\item $\displaystyle\lim_{\theta\to0}\theta\cot \theta$
\answer{$1$}

\item $\displaystyle\lim_{x\to0}\frac{1-\cos x}{\sin x}$
\answer{$0$}

\item $\displaystyle\lim_{\theta\to0}\frac{7\theta}{\sin5\theta}$
\answer{$\displaystyle\frac{7}{5}$}

\item $\displaystyle\lim_{\theta\to0}\frac{7\theta}{\cos5\theta}$
\answer{$0$}

\item $\displaystyle\lim_{x\to0}\frac{\sin x}{x\cos x}$
\answer{$1$}

\item $\displaystyle \lim_{x\to\pi}\frac{\cos x}{x}$
\answer{$\displaystyle -\frac{1}{\pi}$}

\item $\displaystyle \lim_{\theta\to\frac{\pi}{4}}\frac{\tan\theta}{\theta}$
\answer{$\displaystyle \frac{4}{\pi}$}

\item $\displaystyle \lim_{t\to\frac{\pi}{2}}\frac{\sin t-1}{\cos t}$
\answer{$\displaystyle 0$}
\item $\displaystyle \lim_{x\to 0}\frac{\tan x}{x}$
\answer{$\displaystyle 1$}

\item $\displaystyle \lim_{\theta\to\pi}\frac{\cos\theta+1}{\sin^2\theta}$
\answer{$\displaystyle \frac{1}{2}$}

\addtoanswerkey{\end{multicols}}

\end{problemblock}
