Knowledge Organiser: Exact Trig Values
This topic summary covers Knowledge Organiser: Exact Trig Values within Exact Trig Values for GCSE Mathematics. Revise Exact Trig Values in Geometry & Measures for GCSE Mathematics with 14 exam-style questions and 4 flashcards. This topic shows up very often in GCSE exams, so students should be able to explain it clearly, not just recognise the term. It is section 7 of 7 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 7 of 7
Practice
14 questions
Recall
4 flashcards
Knowledge Organiser: Exact Trig Values
Key Terms
- Exact value: An answer expressed as a fraction or surd — no rounding
- Surd: An irrational square root left in exact form (e.g. √2, √3)
- 45-45-90 triangle: The special isosceles right triangle giving values for 45°
- 30-60-90 triangle: Half an equilateral triangle giving values for 30° and 60°
Must-Know Facts (memorise these)
- sin 0° = 0, sin 30° = ½, sin 45° = √2/2, sin 60° = √3/2, sin 90° = 1
- cos is sin in REVERSE: cos 0° = 1, cos 30° = √3/2, cos 60° = ½, cos 90° = 0
- tan 0° = 0, tan 30° = 1/√3, tan 45° = 1, tan 60° = √3, tan 90° = undefined
- Identity: sin²θ + cos²θ = 1 (for any angle)
Key Methods
- Sin pattern: √0/2, √1/2, √2/2, √3/2, √4/2 for 0°, 30°, 45°, 60°, 90°
- Cos = sin reversed
- Tan = sin ÷ cos
- Simplify √2/2 × √2/2 = 2/4 = ½
Key Formulas
- sin 0° = 0, sin 30° = ½, sin 45° = √2/2, sin 60° = √3/2, sin 90° = 1
- cos 0° = 1, cos 30° = √3/2, cos 45° = √2/2, cos 60° = ½, cos 90° = 0
- tan 0° = 0, tan 30° = 1/√3, tan 45° = 1, tan 60° = √3, tan 90° = undefined
Common Mistakes
- Confusing sin and cos values: cos values are sin values in reverse order — use the pattern to check
- tan 90° has no value: tan 90° is undefined — do not write 0 or infinity
- Leaving surd form: When an exact answer is required, write √3/2 not 0.866...
- Simplifying incorrectly: 1/√3 should be rationalised to √3/3 for exact form
Revise this topic interactively on PrepWise — self-test mode, tap-to-reveal definitions, and Common Mistakes from examiners.
Try the interactive Knowledge Organiser — free →Keep building this topic
Read this section alongside the surrounding pages in Exact Trig Values. That gives you the full topic sequence instead of a single isolated revision point.
Practice Questions for Exact Trig Values
What is the exact value of sin 30°?
James says that sin 30° and cos 60° are equal. Is James correct? Explain your answer using exact values.
Quick Recall Flashcards
14 questions on Exact Trig Values — practise free
Instant marking, adaptive difficulty, and 4 spaced repetition flashcards. Free until your GCSEs.
Try PrepWise Free