IGCSEMathsCambridge (CIE)International MathsExtendedExam QuestionsPythagoras & TrigonometryTrigonometric Graphs & Equations

Trigonometric Graphs & Equations (Cambridge (CIE) IGCSE International Maths: Extended): Exam Questions

58 mins21 questions
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1a
Sme Calculator2 marks
Oscillating graph on a set of axes, x axis from 0 to 360 and y axis from -3 to 3. Graph goes through the points (0,3), (90,-3), (180,3), (270,-3) and (360,3).

The graph shows straight f open parentheses x close parentheses equals a cos open parentheses b x close parentheses degree.

Find the value of a and the value of b.

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1b
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Write down the period of straight f left parenthesis x right parenthesis.

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2
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straight f open parentheses x close parentheses equals 3 sin open parentheses 4 x degree close parentheses

Find the amplitude and period of straight f open parentheses x close parentheses.


Amplitude = ................................................

Period = ................................................

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3
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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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4a
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When sin space x degree equals 0.36, find the acute angle x degree.

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4b
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When sin space x degree equals 0.36, find the obtuse angle x degree.

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5a
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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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5b
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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6
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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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7
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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
Sme Calculator3 marks

straight f left parenthesis x right parenthesis equals p cos left parenthesis q x right parenthesis

The amplitude of straight f open parentheses x close parentheses is 3 and the period is 30°.

Find straight f open parentheses 10 close parentheses.

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2
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Solve the equation sin space x equals negative 0.75 for 0 to the power of degree less or equal than x less or equal than 360 degree.

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3
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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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4
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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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5
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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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6a
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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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6b
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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7a
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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7b
Sme Calculator1 mark

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
Graph of y = cos^2(x) from 0 to 360 degrees, showing two complete waves entirely above or on the x axis with peaks at 0, 180 and 360 degrees and troughs at 90 and 270 degrees.

The diagram shows the graph of straight f open parentheses x close parentheses equals open parentheses cos space x degree close parentheses squared for 0 less or equal than x less or equal than 360.

Write down the amplitude and period ofspace straight f left parenthesis x right parenthesis.

Amplitude ................................................

Period ................................................

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2
Sme Calculator2 marks
x-y coordinate plane with x-axis from -360 to 360 and y-axis from -3 to 3. A graph in a negative parabola shape has a maximum point at (0, 3) and meets the x axis at -360 and 360

The diagram shows the graph of straight f open parentheses x close parentheses equals a space cos space open parentheses b x close parentheses for 0 less or equal than x less or equal than 360.

(i) Write down the amplitude and period ofspace straight f left parenthesis x right parenthesis.

Amplitude ................................................

Period ................................................

[2]

(ii) Write down the value of a and b.

[1]

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3
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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4a
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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4b
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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5a
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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5b
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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6
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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7
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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