A-level · Trigonometry

Inverse trigonometric functionsExam-style questions

The functions arcsin, arccos and arctan — why the domains of sin, cos and tan must be restricted to invert them, the principal ranges, and evaluating exact values and composite expressions.

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

DifficultyAllLevel 2Level 3Level 4
  1. 1
    Find, in radians, the exact values of (a) arccos⁡ ⁣(−12)\arccos\!\left(-\frac{1}{2}\right),
    (b) arcsin⁡ ⁣(−22)\arcsin\!\left(-\frac{\sqrt{2}}{2}\right),
    (c) arctan⁡(−1)\arctan(-1).
    Level 3 · 3 marksTry it
  2. 2
    Find the exact value of arcsin⁡ ⁣(sin⁡2π3)\arcsin\!\left(\sin\frac{2\pi}{3}\right).
    Level 3 · 2 marksTry it
  3. 3
    Find the exact value of arccos⁡ ⁣(cos⁡ ⁣(−π4))\arccos\!\left(\cos\!\left(-\frac{\pi}{4}\right)\right).
    Level 3 · 2 marksTry it
  4. 4
    Find the exact value of cos⁡ ⁣(arcsin⁡35)\cos\!\left(\arcsin\frac{3}{5}\right).
    Level 3 · 2 marksTry it
  5. 5
    Find the exact value of sin⁡(arctan⁡2)\sin(\arctan 2).
    Level 3 · 2 marksTry it

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