Special angles

Definition

The special angles 30°, 45° and 60° (together with 0° and 90°) have exact trig values that you work out from two special triangles: a right-angled isosceles triangle with sides 1; 1; √2, and half an equilateral triangle with sides 1; √3; 2.

Worked example

sin 30° = ½, cos 30° = √3/2, tan 45° = 1, sin 60° = √3/2 and cos 60° = ½.

Without a calculator: (sin 60° × tan 45°) ÷ cos 30° = (√3/2 × 1) ÷ (√3/2) = 1.

Where it appears in the exam

Special angles is part of the trigonometry section of CAPS Grade 10 Mathematics and is examined in Paper 2 of the November exam.

Step-by-step method

1. Draw the special triangle for the angle.
2. Label the sides relative to the angle: opposite, adjacent, hypotenuse.
3. Write the ratio from the sides.
4. Simplify, leaving surds in the answer.

Common mistake

Mixing up sin 30° and sin 60°: sin 30° = ½ while sin 60° = √3/2.

Related trigonometry terms

• Reduction formula
• General solution
• Cosine rule
• Sine rule
• Area rule

Frequently asked questions

What does special angles mean in Grade 10 Maths?

The special angles 30°, 45° and 60° (together with 0° and 90°) have exact trig values that you work out from two special triangles: a right-angled isosceles triangle with sides 1; 1; √2, and half an equilateral triangle with sides 1; √3; 2.

Which paper tests special angles in Grade 10?

Special angles belongs to the Trigonometry section of CAPS Grade 10 Mathematics, which is examined in Paper 2 of the November exam.

How do I practise questions involving special angles?

Snap a question that uses special angles into Snap&Learn with your grade set to Grade 10, or work through the Grade 10 topic guide and practice papers.