IGCSEMaths: ExtendedCIEExam QuestionsPythagoras & TrigonometryTrigonometric Graphs & Equations

Syllabus Edition

First teaching 2023

First exams 2025

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Trigonometric Graphs & Equations (CIE IGCSE Maths: Extended)

Exam Questions

44 mins15 questions
Medium
Hard
Very Hard
1
Sme Calculator2 marks

cie-igcse-2020-oct-nov-p4-tz1-q10b

On the diagram, sketch the graph of y space equals space tan space x for 0 degree space less or equal than space x space less or equal than space 360 degree.

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2a
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When sin space x degree equals 0.36, find the acute angle x degree.

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2b
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When sin space x degree equals 0.36, find the obtuse angle x degree.

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3a
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The diagram shows part of a sketch of the curve space y space equals space sin space x degree

q16-paper2h-spec2016-edexcel-igcse-maths

Write down the coordinates of

i)
the point P

ii)
the point Q

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3b
Sme Calculator2 marks

Sketch the graph of y space equals space tan space x for 0 degree space less-than or slanted equal to space x space less-than or slanted equal to space 360 degree

Show the coordinates of any points of intersection with the coordinate axes.

q16b-paper2h-spec2016-edexcel-igcse-maths

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4
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Sketch the graph of y space equals space cos space x degree space for space 0 less-than or slanted equal to space x less-than or slanted equal to space 360

q4-medium-3-12-trigonometric-graphs-and-equations-cie-igcse-maths-extended

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5
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Sketch the graph of y space equals sin space x for 0 degree less than x less than 360 degree

q13a-paper5-nov2020-ocr-gcse-maths

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1
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Solve the equation  tan space x space equals space 2  for  0 degree less or equal than space x space less or equal than space 360 degree .


x space equals ........................   or  x space equals ........................

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2
Sme Calculator3 marks

Solve space 3 tan x equals negative 4 space for 0 degree less or equal than x less or equal than 360 degree.
 

x equals.................. or x equals.................. 

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3
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x degree is an obtuse angle and sin space x degree equals 0.43 .
 
Find the value of x.
 

x = ..............................................

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4a
Sme Calculator4 marks

The grid shows the graph of y space equals space cos space x for 0 degree space less-than or slanted equal to space x space less-than or slanted equal to space 360 degree.

cie-igcse-2020-specimen-p2-q8a
Solve the equation 3 cos space x equals 1 for 0 degree space less-than or slanted equal to space x space less-than or slanted equal to space 360 degree.
Give your answers correct to 1 decimal place.

.................... and ....................

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4b
Sme Calculator1 mark

On the same grid, sketch the graph of y space equals space sin space x for 0 degree space less-than or slanted equal to space x space less-than or slanted equal to space 360 degree.

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5a
Sme Calculator1 mark

Here is a sketch of space y space equals space cos space x spacefor values of x from 0° to 360°

q27-paper-1h-nov-2018-aqa-gcse-maths

alpha degree is an acute angle.
cos space alpha degree space equals space k

Circle the value of cos space left parenthesis 180 degree space – space alpha degree right parenthesis

1 space – space k k – k – 1 space – space k

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5b
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Circle the value of cos spaceleft parenthesis 360 degree space plus space alpha degree right parenthesis

k space – space 1 k space plus space 1 – k k

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1
Sme Calculator2 marks

The diagrams show the graph of a function.
 
Write down the function.

cie-igcse-2020-may-jun-p4-tz3-q10aii 

straight f open parentheses x close parentheses equals................................................

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2a
Sme Calculator4 marks
i)
On the axes, sketch the graph of  y equals sin space x  for  0 degree less or equal than x less or equal than 360 degree.

cie-igcse-2020-may-june-p4-tz1-q8

[2]

ii)
Describe fully the symmetry of the graph of  y equals sin space x  for  0 degree less or equal than x less or equal than 360 degree.

[2]

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2b
Sme Calculator3 marks

Solve  4 space sin space x minus 1 equals 2  for  0 degree less or equal than x less or equal than 360 degree.


x equals ........................ and x equals ......................

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3a
Sme Calculator2 marks

cie-igcse-2020-march-p2-tz2-q19a

On the diagram, sketch the graph of y equals cos space x for 0 degree less or equal than x less or equal than 360 degree.

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3b
Sme Calculator3 marks
Solve the equation 4 cos space x plus 2 equals 3 for 0 degree less or equal than x less or equal than 360 degree.



x equals .................... and x equals ....................

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4
Sme Calculator3 marks

Solve the equation  5 space tan space x space equals space minus 7  for  0 degree space less or equal than space x space less or equal than space 360 degree.

    

 x space equals space.................... or space x space equals space....................

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5
Sme Calculator1 mark

y spaceis an obtuse angle.

Which statement is true?
Tick one box.

square sin space y space greater than space 0 and cos space y space greater than space 0
square sin space y space greater than space 0 spaceand cos space y space less than space 0
square sin space y space less than space 0 space andspace cos space y space greater than space 0
square sin space y space less than space 0 and cos space y space less than space 0

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