A-level · Trigonometry

Exact values of trigonometric ratiosExam-style questions

The exact surd values of sin, cos and tan at 0, 30, 45, 60 and 90 degrees, where they come from (two special triangles plus the unit circle), the sine ladder that rebuilds the whole table, and how to answer "find the exact value" questions without a calculator.

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6 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAllLevel 2Level 3
  1. 1
    Write down the exact value of cos⁡30∘\cos 30^\circ.
    Level 3 · 1 markTry it
  2. 2
    Write down the exact values of sin⁡60∘\sin 60^\circ and tan⁡60∘\tan 60^\circ.
    Level 3 · 2 marksTry it
  3. 3
    Write down the exact value of sin⁡45∘\sin 45^\circ, rationalising the denominator.
    Level 3 · 1 markTry it
  4. 4
    Find the exact value of sin⁡30∘+cos⁡60∘+tan⁡45∘\sin 30^\circ + \cos 60^\circ + \tan 45^\circ.
    Level 3 · 2 marksTry it