Mathematics 10 — Exercise 7.1 · Q3 (vii)

Full question

Without a calculator evaluate sin 135° exactly.

Step-by-step solution

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

   $$180-135=45$$

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

   $$\sin \left(\mathrm{135°}\right)=\sin \left(\mathrm{45°}\right)$$

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

   $$\sin \left(\mathrm{135°}\right)=\frac{1}{2}\times \sqrt{2}$$

Answer

The final answer is shown below.