Robinson Tuition
Grade 6 · Higher · free GCSE maths worksheet

Exact values of trigonometric ratios

sin, cos and tan of 0, 30, 45, 60 and 90 degrees.

15 original questions, 41 marks. Print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

Worksheet PDFWorked solutions PDFAnswers PDF

The questions

1

Write down the exact value of sin 30°.

1 mark
Show answer
12
2

Write down the exact value of

  1. cos 30°
  2. sin 45°
  3. tan 60°
3 marks
Show answer
a) √3/2 b) 1/√2 or √2/2 c) √3
3

Write down the exact value of tan 45°.

1 mark
Show answer
1
4

x is an acute angle. Use exact values to find x when

  1. sin x = 12
  2. cos x = 12
  3. tan x = 1
3 marks
Show answer
a) 30° b) 60° c) 45°
5

Work out the exact value of sin 60° × cos 30°.

Give your answer as a fraction.

2 marks
Show answer
34
6

Show that sin 60° ÷ tan 60° = cos 60°

2 marks
Show answer
1/2
7

Work out the exact value of (sin 30° + cos 60°) × tan 60°.

2 marks
Show answer
√3
8

An equilateral triangle has sides of length 10 cm.

  1. Use trigonometry to show that the height of the triangle is 5√3 cm.
  2. Work out the exact area of the triangle.
4 marks
Show answer
a) height = 10 × sin 60° = 5√3 cm b) 25√3 cm²
9

A square has sides of length 8 cm. Use trigonometry to show that its diagonal is 8√2 cm.

3 marks
Show answer
8√2 cm
10

In triangle ABC, angle ABC = 90° and angle BAC = 30°.

AC = 14 cm.

Without using a calculator, work out the length of BC.

You must show your working.

14 cm30°ABCDiagram NOT accurately drawn
3 marks
Show answer
7 cm
11

In triangle PQR, angle PQR = 90° and angle QPR = 45°.

PQ = 8 cm.

Without using a calculator, work out the exact length of PR.

Give your answer in the form k√2.

8 cm45°PQRDiagram NOT accurately drawn
3 marks
Show answer
8√2 cm
12

In triangle DEF, angle DEF = 90° and angle EDF = 60°.

DE = 5 cm.

Without using a calculator, work out the exact length of EF.

5 cm60°DEFDiagram NOT accurately drawn
3 marks
Show answer
5√3 cm
13

In triangle JKL, angle JKL = 90°.

JK = 6 cm and JL = 12 cm.

Without using a calculator, find the size of angle JLK.

You must show your working.

6 cm12 cmJKLDiagram NOT accurately drawn
3 marks
Show answer
30°
14

Work out the exact value of

tan 30° × tan 60° + cos 45° × sin 45°

Give your answer as a fraction.

3 marks
Show answer
32
15

ABCD is a trapezium in which AB is parallel to DC.

Angle ADC = 90°, angle BCD = 60°, AB = 6 cm and DC = 10 cm.

Without using a calculator, work out the exact area of the trapezium.

Give your answer in the form k√3 cm2.

6 cm10 cm60°ABCDDiagram NOT accurately drawn
5 marks
Show answer
32√3 cm²

Every question here is original and written by Robinson Tuition. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper.

All Grade 6 topics