Advanced Trigonometry, SMB-021

Complete the table of exact values. (3 marks)

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\begin{array}{|c|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} \theta \rule[-1ex]{0pt}{0pt}& \ \ 0^{\circ} \ \ & 30^{\circ} & 45^{\circ} & 60^{\circ} & \ 90^{\circ} \ \\
\hline
\rule{0pt}{3.5ex} \sin \theta \rule[-3ex]{0pt}{0pt}& 0 & \quad & \quad & \dfrac{\sqrt{3}}{2} & 1 \\
\hline
\rule{0pt}{4ex} \cos \theta \rule[-2.5ex]{0pt}{0pt}& \quad & \quad & \dfrac{1}{\sqrt{2}} & \dfrac{1}{2} & 0 \\
\hline
\rule{0pt}{3.5ex} \tan \theta \rule[-3ex]{0pt}{0pt}& \quad & \dfrac{1}{\sqrt{3}} & 1 & \quad & \infty \\
\hline
\end{array}

Show Answers Only

\begin{array}{|c|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} \theta \rule[-1ex]{0pt}{0pt}& \ \ 0^{\circ} \ \ & 30^{\circ} & 45^{\circ} & 60^{\circ} & \ 90^{\circ} \ \\
\hline
\rule{0pt}{3.5ex} \sin \theta \rule[-3ex]{0pt}{0pt}& 0 & \dfrac{1}{2} & \dfrac{1}{\sqrt{2}} & \dfrac{\sqrt{3}}{2} & 1 \\
\hline
\rule{0pt}{4ex} \cos \theta \rule[-2.5ex]{0pt}{0pt}& 1 & \dfrac{\sqrt{3}}{2} & \dfrac{1}{\sqrt{2}} & \dfrac{1}{2} & 0 \\
\hline
\rule{0pt}{3.5ex} \tan \theta \rule[-3ex]{0pt}{0pt}& 0 & \dfrac{1}{\sqrt{3}} & 1 & \sqrt{3} & \infty \\
\hline
\end{array}

Show Worked Solution

\begin{array}{|c|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} \theta \rule[-1ex]{0pt}{0pt}& \ \ 0^{\circ} \ \ & 30^{\circ} & 45^{\circ} & 60^{\circ} & \ 90^{\circ} \ \\
\hline
\rule{0pt}{3.5ex} \sin \theta \rule[-3ex]{0pt}{0pt}& 0 & \dfrac{1}{2} & \dfrac{1}{\sqrt{2}} & \dfrac{\sqrt{3}}{2} & 1 \\
\hline
\rule{0pt}{4ex} \cos \theta \rule[-2.5ex]{0pt}{0pt}& 1 & \dfrac{\sqrt{3}}{2} & \dfrac{1}{\sqrt{2}} & \dfrac{1}{2} & 0 \\
\hline
\rule{0pt}{3.5ex} \tan \theta \rule[-3ex]{0pt}{0pt}& 0 & \dfrac{1}{\sqrt{3}} & 1 & \sqrt{3} & \infty \\
\hline
\end{array}