GCSE · Pythagoras & right-angled trigonometry

Exact trig values (sin, cos and tan of 0°, 30°, 45°, 60° and 90°)Exam-style questions

Where the exact values of sin, cos and tan come from: two triangles you can sketch in seconds, half a square and half an equilateral triangle, plus a ladder lying flat or standing upright for 0° and 90°. How to use them to find an exact side in surd form, how to get an angle back from an exact ratio, and how to answer a non-calculator "show that" with exact values.

Start practising Read the lesson

20 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3 Level 4 Level 5

1
The diagram shows a right-angled triangle.Diagram NOT accurately drawn

Work out the value of $x$ .

(2 marks)
Level 2 · 2 marksTry it
2
The diagram shows a right-angled triangle.Not to scale

Work out the exact length of $x$ .

(2 marks)
Level 2 · 2 marksTry it
3
A straight slide in a playground is $4.8$ m long.

The top of the slide is $2.4$ m above the level ground.

The bottom of the slide is on the ground.

Work out the angle the slide makes with the ground.

(2 marks)
Level 2 · 2 marksTry it
4
The diagram shows a right-angled triangle.Diagram NOT accurately drawn

Work out the value of $x$ . (2 marks)
Level 3 · 2 marksTry it
5
Mei says,

" $\sin 60°$ is twice $\sin 30°$ , because $60$ is twice $30$ ."

Is Mei correct?

Show how you decide.

(2 marks)
Level 3 · 2 marksTry it

15 more questions on exact trig values (sin, cos and tan of 0°, 30°, 45°, 60° and 90°)

Free with an account — just an email, no card. The whole bank, every mark scheme and worked solution.

Start free