An isosceles right triangle with legs 1 has hypotenuse 2. Its acute angles are 45. Bisecting an equilateral triangle of side 2 gives sides 1, 3,2, with angles 30,60,90. Use opposite, adjacent and hypotenuse to reconstruct exact values. **Angle** | **0 ** | **30 ** | **45 ** | **60 ** | **90 ** sin | 0 | 1/2 | 2/2 | 3/2 | 1 cos | 1 | 3/2 | 2/2 | 1/2 | 0 tan | 0 | 3/3 | 1 | 3 | Undefined Keep these values exact when no approximation is requested. Tangent is undefined at 90, because its cosine denominator is zero; it is not a very large finite number.

An isosceles right triangle with legs 1 has hypotenuse \(\sqrt2\). Its acute angles are \(45^\circ\). Bisecting an equilateral triangle of side 2 gives sides \(1,\sqrt3,2\), with angles \(30^\circ,60^\circ,90^\circ\). Use opposite, adjacent and hypotenuse to reconstruct exact values.

Keep these values exact when no approximation is requested. Tangent is undefined at \(90^\circ\), because its cosine denominator is zero; it is not a very large finite number.

Trigonometry

Cambridge IGCSE Mathematics 0580. Initial catalogue covers the assessed demands of February/March 2026 Paper 22; further Core and Extended mappings require paper-level scope review.

Angle	\(0^\circ\)	\(30^\circ\)	\(45^\circ\)	\(60^\circ\)	\(90^\circ\)
sin	0	1/2	\(\sqrt2/2\)	\(\sqrt3/2\)	1
cos	1	\(\sqrt3/2\)	\(\sqrt2/2\)	1/2	0
tan	0	\(\sqrt3/3\)	1	\(\sqrt3\)	Undefined

Exact values from special triangles

Exact values from special triangles