Discia GCSE Maths › Geometry & Measures › Exact trig values

Exact trig values worksheet

10 GCSE practice questions with answers, free to print. Every sheet is generated, so you can make a fresh one whenever you need it.

10 questions 20 marks Sheet 1
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  1. 1 mark

    Write down the exact value of \(\sin 45^\circ\).

    You must not use a calculator.

  2. 2 marks Part of a table of exact trigonometric values is shown below.
    \(x\)\(\sin x\)\(\cos x\)\(\tan x\)
    \(30^\circ\)\(\frac{1}{2}\)
    Complete the row. Give each value exactly. You must not use a calculator.
  3. 2 marks

    Work out the exact value of \(\tan 45^\circ + \cos 0^\circ\).

    You must not use a calculator.

  4. 2 marks

    \(x\) is a number with \(0 \leq x \leq 90\).

    Solve \(\cos x^\circ = 0\).

    You must not use a calculator.

  5. 3 marks

    \(ABC\) is a right-angled triangle.

    Angle \(ABC = 90^\circ\), angle \(BAC = 30^\circ\) and \(AC = 12\) cm.

    (a)

    State the exact value of \(\sin 30^\circ\).

    (b)

    Work out the exact length of \(BC\).

  6. 1 mark

    Write down the exact value of \(\sin 60^\circ\).

    You must not use a calculator.

  7. 2 marks Here is part of a table of exact trigonometric values.
    \(x\)\(\sin x\)\(\cos x\)\(\tan x\)
    \(0^\circ\)\(0\)
    Complete the row. Give each value exactly, without using a calculator.
  8. 2 marks

    Work out the exact value of \(\sin 60^\circ \times \cos 30^\circ\).

    You must not use a calculator.

  9. 2 marks

    \(x\) is a number with \(0 \leq x \leq 90\).

    Solve \(\cos x^\circ = \frac{1}{2}\).

    You must not use a calculator.

  10. 3 marks

    \(ABC\) is a right-angled triangle.

    Angle \(ABC = 90^\circ\), angle \(BAC = 60^\circ\) and \(AC = 14\) cm.

    (a)

    State the exact value of \(\sin 60^\circ\).

    (b)

    Calculate the exact length of \(BC\).

Answers

  1. \(\frac{\sqrt{2}}{2}\)
  2. \(\cos 30^\circ = \frac{\sqrt{3}}{2}\) and \(\tan 30^\circ = \frac{\sqrt{3}}{3}\)
  3. \(2\)
  4. \(90\)
  5. (a) \(\frac{1}{2}\)
    (b) \(6\) cm
  6. \(\frac{\sqrt{3}}{2}\)
  7. \(\sin 0^\circ = 0\) and \(\cos 0^\circ = 1\)
  8. \(\frac{3}{4}\)
  9. \(60\)
  10. (a) \(\frac{\sqrt{3}}{2}\)
    (b) \(7\sqrt{3}\) cm

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