Trigonometry Cheat Sheet

Trigonometry Cheat Sheet

Quick Revision

Trigonometry relates the angles of a right-angled triangle to the ratios of its sides. Learn the six ratios, the standard-angle values and the three identities, and most questions fall quickly.

Ready to practise? Take the Trigonometry quiz

1. The Six Ratios

For a right-angled triangle, relative to an angle θ (P = perpendicular, B = base, H = hypotenuse):

Also: tan θ = sin θ / cos θ and cot θ = cos θ / sin θ.

2. Standard-Angle Values

A memory aid for sine: √0/2, √1/2, √2/2, √3/2, √4/2 for 0°, 30°, 45°, 60°, 90°. Cosine is the same list reversed.

3. Pythagorean Identities

sin²θ + cos²θ = 1
1 + tan²θ = sec²θ
1 + cot²θ = cosec²θ

4. Complementary Angles

Ratios of an angle and its complement (90° − θ) swap in pairs:

sin(90° − θ) = cos θ        cos(90° − θ) = sin θ
tan(90° − θ) = cot θ        cot(90° − θ) = tan θ
sec(90° − θ) = cosec θ      cosec(90° − θ) = sec θ

5. Height and Distance

• Angle of elevation — you look up at an object.
• Angle of depression — you look down at an object.

These problems use tan θ = height / distance, so a known angle (often 30°, 45° or 60°) and one measurement give the other.

Example

From 30 m away, the angle of elevation of a tower's top is 45°.

tan 45° = height / 30 → 1 = height / 30 → height = 30 m

6. Exam Quick Tips

• Memorise the standard-angle table; most questions start there.
• Keep the three identities ready — especially sin²θ + cos²θ = 1.
• For a complement (90° − θ), sin ↔ cos, tan ↔ cot, sec ↔ cosec.
• In height-and-distance, draw the triangle and use tan θ = height / distance.

Keep revising with the rest of the Maths section:

• All Maths topics
• Geometry Cheat Sheet
• Mensuration Cheat Sheet

How this was made: Drafted with AI assistance; spot-checked by the editor on 31 October 2026.