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GCSEFurther MathsAQAExam Questions6. GeometryTrigonometric Graphs & Equations

Trigonometric Graphs & Equations (AQA GCSE Further Maths): Exam Questions

46 mins15 questions

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1a
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Here is a sketch of y equals tan space x for space 0 degree less-than or slanted equal to x less-than or slanted equal to 360 degree

q13a-2018-paper-2-aqa-gcse-further-maths

How many solutions of tan space x equals k where k greater than 0 are between 90° and 360° ?

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1b
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0 less than p less than 1

How many solutions of sin space x equals p – 1 are between 0° and 180° ?

You may use a sketch graph to help you.

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1c
Sme Calculator2 marks

State the coordinates of each point where the graph y equals cos space x for 0 degree less-than or slanted equal to x less-than or slanted equal to 360 degree meets or intersects an axis.

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2
Sme Calculator2 marks

6 sin squared space x plus 4 cos squared space x identical to straight A plus straight B space cos squared space x where straight A and straight B are integers.

Work out the values of straight A and straight B.

You must show your working.

straight A = ..........................

straight B = ...........................

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3
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Work out the two values ofspace x spacefor which

sin space x equals 1 half

where 0 degree less-than or slanted equal to x less-than or slanted equal to 360 degree 

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4
Sme Calculator2 marks

Work out the two values ofspace x spacefor which

cos space x equals 1 half

where 0 degree less-than or slanted equal to x less-than or slanted equal to 360 degree 

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5
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2 sin space x minus 5 cos space x equals 0

Find the value of tan space x.

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1a
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Show that  2 cos squared space theta identical to 2 minus 2 sin squared space theta

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1b
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Hence, solve  2 cos squared space theta plus 3 sin space theta equals 3  for  0 less than theta less than 180 degree

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2
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Here is a sketch of  y equals sin space x  for  0 degree less-than or slanted equal to x less-than or slanted equal to 360 degree

q6-paper1-nov2021-aqa-gcse-furthermaths

You are given that sin space 220 degree equals – k

Work out the two values ofspace x spacefor 0 degree less-than or slanted equal to x less-than or slanted equal to 360 degree for which  y equals k

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3
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Work out the value of x where  0 degree less-than or slanted equal to x less-than or slanted equal to 90 degree for which 3 tan squared space x equals 1

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4
Sme Calculator2 marks

Here is a sketch graph of y equals cos space x for  0 degree less-than or slanted equal to x less-than or slanted equal to 360 degree

q15-2019-paper-1-aqa-gcse-further-maths

You are given that   cos space 36 degree equals 0.8090

Solve cos space x equals negative 0.8090    for   0 degree less-than or slanted equal to x less-than or slanted equal to space 360 degree

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5
Sme Calculator3 marks

8 cos space x plus 5 sin space x space equals space 0 where 90 degree less than x less than 180 degree

Work out the size of angle x.

 ........................ degrees

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6a
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Prove that  sin squared space x minus 3 cos to the power of 2 space end exponent x identical to 4 sin squared space x minus 3.

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6b
Sme Calculator4 marks

Hence, or otherwise, work out the values of x between 0 degreeand 360 degree for which sin squared space x minus 3 cos squared space x equals 0.

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1
Sme Calculator4 marks

Show that fraction numerator 2 sin space x plus cos space x over denominator tan space x end fraction minus fraction numerator 1 over denominator sin space x end fraction can be written in the form    a cos space x plus b sin space x

where a and bare integers.

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2a
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Show that fraction numerator 2 sin squared space x minus 1 plus cos squared space x over denominator sin space x space cos space x end fraction is equivalent to tan x

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2b
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Hence solve fraction numerator 2 sin squared space x minus 1 plus cos squared space x over denominator sin space x space cos space x end fraction equals negative 1  for  0 degree less-than or slanted equal to x less-than or slanted equal to 360 degree

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3
Sme Calculator4 marks

Angle theta is obtuse and sin space theta equals fraction numerator square root of 11 over denominator 6 end fraction.

Work out the value of cos space theta.

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4
Sme Calculator1 mark

Angle x is acute.

tan space x equals fraction numerator p plus 1 over denominator p minus 1 end fraction where p is a constant greater than 1

Which of the statements below is correct?

Circle your answer.

x equals 45 degree       x less than 45 degree       x greater than 45 degree       x could be any acute angle

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