IGCSE Math RevisionQuestion 1
Without a calculator, find the value of \(\sin 30° + \cos 60°\).
Show the worked answer
- \(\sin 30° = \frac{1}{2}\) and \(\cos 60° = \frac{1}{2}\).
Answer: \(1\)
Cambridge IGCSE Maths (0580) · Topic 6: Trigonometry · 6.3
Cambridge IGCSE Maths 0580 Exact Trigonometric Values Questions
Exact Trigonometric Values questions with worked answers for Cambridge IGCSE Mathematics (0580). Each question says whether it is Core or Extended and whether it is for a calculator or non-calculator paper. Try each one before you open the answer.
- 9 questions
- 9 Extended
- 9 non-calculator
- Free, no sign-in
What the syllabus asks
- 6.3 Exact trigonometric values Extended only
Extended: Exact values of sin and cos of 0°, 30°, 45°, 60° and 90°, and of tan of 0°, 30°, 45° and 60°.
Summarised in our own words: check the exact wording in the official 0580 syllabus.
Exact Trigonometric Values questions: Extended
Extended content, for Papers 2 and 4.
Question 2
Write down the exact value of \(\cos 30°\).
Show the worked answer
- From the half-equilateral triangle with sides \(1\), \(\sqrt{3}\) and \(2\): \(\cos 30° = \frac{\sqrt{3}}{2}\).
Answer: \(\frac{\sqrt{3}}{2}\)
Question 3
Without using a calculator, write down the exact value of
(a) \(\cos 30^\circ\) (b) \(\sin 45^\circ\).
Show the answer and mark scheme
- B1 (a) √3/2
- B1 (b) √2/2 or 1/√2
Answer: (a) \(\frac{\sqrt{3}}{2}\) (b) \(\frac{\sqrt{2}}{2}\)
Question 4
Without a calculator, find the value of \(\frac{\tan 60°}{\tan 30°}\).
Show the worked answer
- \(\tan 60° = \sqrt{3}\) and \(\tan 30° = \frac{1}{\sqrt{3}}\).
- \(\sqrt{3} \div \frac{1}{\sqrt{3}} = \sqrt{3} \times \sqrt{3} = 3\)
Answer: \(3\)
Question 5
A right-angled triangle has a hypotenuse of \(12\) cm and an angle of \(30°\).
Find the exact lengths of the other two sides.
Show the worked answer
- Opposite \(30°\): \(12 \sin 30° = 12 \times \frac{1}{2} = 6\) cm.
- Adjacent: \(12 \cos 30° = 12 \times \frac{\sqrt{3}}{2} = 6\sqrt{3}\) cm.
Answer: \(6\) cm and \(6\sqrt{3}\) cm
Question 6
Without using a calculator, find the exact value of \(\sin 30^\circ + \cos 60^\circ\).
Show the answer and mark scheme
- M1 ½ + ½
- A1 1
Answer: \(1\)
Question 7
Without a calculator, find the exact value of \(\sin^2 45° + \cos^2 30°\).
Show the worked answer
- \(\sin 45° = \frac{\sqrt{2}}{2}\), so \(\sin^2 45° = \frac{1}{2}\).
- \(\cos^2 30° = \frac{3}{4}\).
- \(\frac{1}{2} + \frac{3}{4} = \frac{5}{4}\)
Answer: \(\frac{5}{4}\)
Question 8
\(x\) is an acute angle and \(\sin x = \frac{\sqrt{3}}{2}\).
Find \(x\) and the exact value of \(\tan x\).
Show the worked answer
- \(\sin 60° = \frac{\sqrt{3}}{2}\), so \(x = 60°\).
- \(\tan 60° = \sqrt{3}\).
Answer: \(x = 60°\), \(\tan x = \sqrt{3}\)
Question 9
Without using a calculator, solve these equations for \(0^\circ \le x \le 90^\circ\).
(a) \(\sin x = \dfrac{\sqrt{3}}{2}\) (b) \(\tan x = \dfrac{1}{\sqrt{3}}\)
Show the answer and mark scheme
- B1 (a) 60°
- B1 (b) 30°
Answer: (a) \(60^\circ\) (b) \(30^\circ\)
Every question on this page is original, written for IGCSE Math Revision rather than taken from Cambridge papers, and each answer was re-solved independently before publishing. Questions with a mark scheme come from our 0580 practice bank (M method, A accuracy, B independent marks).
Keep going
- Trigonometry practice for 0580: more questions, each one marked, tagged Core or Extended
- My mistakes, then a Skill Builder on the skills you missed
- Common mistakes in 0580: what the Cambridge examiner reports say
- Trigonometry revision notes and the 0580 formula sheet
- Cambridge IGCSE Maths 0580 past papers, when you are ready for a full paper
Questions students ask
Which Cambridge 0580 papers can test exact trigonometric values?
Exact Trigonometric Values is Extended content (syllabus 6.3), so it is tested only on the Extended papers, Paper 2 (non-calculator) and Paper 4 (calculator). Core candidates do not need it.
Are these Cambridge past-paper questions?
No. Every question here was written for IGCSE Math Revision in the style of the 0580 papers, and each answer was checked independently before publishing. For real exam practice, use the Cambridge past papers linked from our 0580 past papers page.
Where can I practise more exact trigonometric values questions?
In the 0580 practice for topic 6 (Trigonometry), where every question is marked and tagged Core or Extended. Practice is part of the IGCSE plan, with a free preview; the questions on this page are free.