Find the value of $\tan 30 °$ without using a calculator.

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Solution

Calculate the value of $\tan 30 °$ .
Expand the expression in terms of sine and cosine.
$\begin{array}{rcl} \tan 30 ° & = & \frac{\sin 30 °}{\cos 30 °} \\ = & \frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}} \\ = & \frac{1}{\sqrt{3}} \end{array}$
Hence, the required final answer is $\frac{1}{\sqrt{3}}$ .

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