Mathematics 10 — Exercise 7.1 · Q3 (ii)

Full question

Without a calculator evaluate tan 150° exactly.

Step-by-step solution

1. The angle lies in quadrant II. Subtract it from 180° to find the reference angle.

   $$180-150=30$$

2. Use the supplementary-angle identity and its quadrant sign.

   $$\tan \left(\mathrm{150°}\right)=-\tan \left(\mathrm{30°}\right)$$

3. Insert the exact 30°, 45° or 60° value and simplify the fraction or root.

   $$\tan \left(\mathrm{150°}\right)=\left(-\frac{1}{3}\right)\times \sqrt{3}$$

Answer

The final answer is shown below.