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.
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1 mark
Write down the exact value of \(\sin 45^\circ\).
You must not use a calculator.
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2 marks
Part of a table of exact trigonometric values is shown below.
Complete the row. Give each value exactly. You must not use a calculator.\(x\) \(\sin x\) \(\cos x\) \(\tan x\) \(30^\circ\) \(\frac{1}{2}\) -
2 marks
Work out the exact value of \(\tan 45^\circ + \cos 0^\circ\).
You must not use a calculator.
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2 marks
\(x\) is a number with \(0 \leq x \leq 90\).
Solve \(\cos x^\circ = 0\).
You must not use a calculator.
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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 \(BC\).
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1 mark
Write down the exact value of \(\sin 60^\circ\).
You must not use a calculator.
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2 marks
Here is part of a table of exact trigonometric values.
Complete the row. Give each value exactly, without using a calculator.\(x\) \(\sin x\) \(\cos x\) \(\tan x\) \(0^\circ\) \(0\) -
2 marks
Work out the exact value of \(\sin 60^\circ \times \cos 30^\circ\).
You must not use a calculator.
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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.
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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
- \(\frac{\sqrt{2}}{2}\)
- \(\cos 30^\circ = \frac{\sqrt{3}}{2}\) and \(\tan 30^\circ = \frac{\sqrt{3}}{3}\)
- \(2\)
- \(90\)
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(a) \(\frac{1}{2}\)
(b) \(6\) cm - \(\frac{\sqrt{3}}{2}\)
- \(\sin 0^\circ = 0\) and \(\cos 0^\circ = 1\)
- \(\frac{3}{4}\)
- \(60\)
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(a) \(\frac{\sqrt{3}}{2}\)
(b) \(7\sqrt{3}\) cm