Advanced Trigonometry, SMB-020

Using the right-angled triangles above, or otherwise, complete the table below. (3 marks)

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\begin{array}{|c|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} \theta \rule[-1ex]{0pt}{0pt}& \ 30^{\circ} \ & \ 45^{\circ} \ & \ 60^{\circ}\ \\
\hline
\rule{0pt}{4.5ex} \sin \theta \rule[-3ex]{0pt}{0pt}& \dfrac{1}{2} & \dfrac{1}{\sqrt{2}} &\quad\\
\hline
\rule{0pt}{4.5ex} \cos \theta \rule[-3ex]{0pt}{0pt}& \dfrac{\sqrt{3}}{2}& \quad & \quad \\
\hline
\rule{0pt}{3.5ex} \tan \theta \rule[-2.5ex]{0pt}{0pt}& \quad & 1 & \sqrt{3} \\
\hline
\end{array}

Show Answers Only

\begin{array}{|c|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} \theta \rule[-1ex]{0pt}{0pt}& \ 30^{\circ} \ & \ 45^{\circ} \ & \ 60^{\circ}\ \\
\hline
\rule{0pt}{4.5ex} \sin \theta \rule[-3ex]{0pt}{0pt}& \dfrac{1}{2} & \dfrac{1}{\sqrt{2}} & \dfrac{\sqrt{3}}{2} \\
\hline
\rule{0pt}{4.5ex} \cos \theta \rule[-3ex]{0pt}{0pt}& \dfrac{\sqrt{3}}{2} & \dfrac{1}{\sqrt{2}} & \dfrac{1}{2} \\
\hline
\rule{0pt}{3.5ex} \tan \theta \rule[-3ex]{0pt}{0pt}& \dfrac{1}{\sqrt{3}} & 1 & \sqrt{3} \\
\hline
\end{array}

Show Worked Solution

\begin{array}{|c|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} \theta \rule[-1ex]{0pt}{0pt}& \ 30^{\circ} \ & \ 45^{\circ} \ & \ 60^{\circ}\ \\
\hline
\rule{0pt}{4.5ex} \sin \theta \rule[-3ex]{0pt}{0pt}& \dfrac{1}{2} & \dfrac{1}{\sqrt{2}} & \dfrac{\sqrt{3}}{2} \\
\hline
\rule{0pt}{4.5ex} \cos \theta \rule[-3ex]{0pt}{0pt}& \dfrac{\sqrt{3}}{2} & \dfrac{1}{\sqrt{2}} & \dfrac{1}{2} \\
\hline
\rule{0pt}{3.5ex} \tan \theta \rule[-3ex]{0pt}{0pt}& \dfrac{1}{\sqrt{3}} & 1 & \sqrt{3} \\
\hline
\end{array}