PremiumDaniel R. A Level Maths tutor, A Level Further Mathematics  tutor, GC...

Daniel R.

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Mathematics (Bachelors) - Durham University

5.0
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108 reviews

This tutor is also part of our Schools Programme. They are trusted by teachers to deliver high-quality 1:1 tuition that complements the school curriculum.

113 completed lessons

About me

I’m a third year student studying Maths with European Studies at Durham. In my A levels, I achieved A* in Maths and Further Maths and have had experience teaching new spec GCSE and A-level, so I am familiar with the course content and what the examiners are looking for in answers and can help you achieve the top grades.  In the past I have helped friends at GCSE and A level, including leading group A-level Maths revision sessions. I am enthusiastic about all the subjects I offer and I hope I can impart some of that enthusiasm on to you.

I’m a third year student studying Maths with European Studies at Durham. In my A levels, I achieved A* in Maths and Further Maths and have had experience teaching new spec GCSE and A-level, so I am familiar with the course content and what the examiners are looking for in answers and can help you achieve the top grades.  In the past I have helped friends at GCSE and A level, including leading group A-level Maths revision sessions. I am enthusiastic about all the subjects I offer and I hope I can impart some of that enthusiasm on to you.

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About my sessions

In the session I aim to use a variety of teaching methods, including past paper questions and diagrams to promote engagement and enhance learning so that you get the most out of your session. Everyone learns differently so I believe that it is important to tailor the pace and content of the session to you, with specific focus being placed on the areas which you feel unsure about and wish to improve upon.

In the session I aim to use a variety of teaching methods, including past paper questions and diagrams to promote engagement and enhance learning so that you get the most out of your session. Everyone learns differently so I believe that it is important to tailor the pace and content of the session to you, with specific focus being placed on the areas which you feel unsure about and wish to improve upon.

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Personally interviewed by MyTutor

We only take tutor applications from candidates who are studying at the UK’s leading universities. Candidates who fulfil our grade criteria then pass to the interview stage, where a member of the MyTutor team will personally assess them for subject knowledge, communication skills and general tutoring approach. About 1 in 7 becomes a tutor on our site.

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Ratings & Reviews

5from 108 customer reviews
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Stephanie (Parent from Tunbridge Wells)

May 8 2017

Huge help!

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Anujin (Student)

October 12 2016

Thanks again!

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Anujin (Student)

October 20 2016

Another great tutorial, thank you very much!

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Mrs E (Parent from Milton Keynes)

June 25 2016

AAA++++

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Qualifications

SubjectQualificationGrade
MathsA-level (A2)A*
Further MathsA-level (A2)A*
PhysicsA-level (A2)A
FrenchA-level (A2)A

General Availability

Pre 12pm12-5pmAfter 5pm
mondays
tuesdays
wednesdays
thursdays
fridays
saturdays
sundays

Subjects offered

SubjectQualificationPrices
Further MathematicsA Level£26 /hr
MathsA Level£26 /hr
MathsGCSE£24 /hr
PhysicsGCSE£24 /hr

Questions Daniel has answered

How do I express y=acosx+bsinx in the form y=Rcos(x-c)?

From the addition formula, we know that:

Rcos(x-c) = Rcos(x)sin(c)+Rsin(x)cos(c)

Therefore:

acos(x)+bsin(x) = Rcos(x)cos(c)+Rsin(x)sin(c)

If we equate the coefficients of cos(x) and sin(x) we see that:

acos(x) = Rcos(x)sin(c);   therefore a = Rcos(c)

And that:

bsin(x) = Rsin(x)cos(c);    therefore b = Rsin(c)

To find c:

If we divide one of the above results by the other:

Rsin(c)/Rcos(c) = b/a

Rsin(c)/Rcos(c) = b/a

tan(c) = b/a

Therefore, c = arctan(b/a)

To find R:

a2+b2 = R2cos2(c)+R2sin2(c)

a2+b2 = R2(cos2(c)+sin2(c))

As cos2(c)+sin2(c) = 1,

a2+b2 = R2

(a2+b2)1/2=R

So, overall:

acos(x)+bsin(x) = (a2+b2)1/2cos(x-arctan(b/a))

From the addition formula, we know that:

Rcos(x-c) = Rcos(x)sin(c)+Rsin(x)cos(c)

Therefore:

acos(x)+bsin(x) = Rcos(x)cos(c)+Rsin(x)sin(c)

If we equate the coefficients of cos(x) and sin(x) we see that:

acos(x) = Rcos(x)sin(c);   therefore a = Rcos(c)

And that:

bsin(x) = Rsin(x)cos(c);    therefore b = Rsin(c)

To find c:

If we divide one of the above results by the other:

Rsin(c)/Rcos(c) = b/a

Rsin(c)/Rcos(c) = b/a

tan(c) = b/a

Therefore, c = arctan(b/a)

To find R:

a2+b2 = R2cos2(c)+R2sin2(c)

a2+b2 = R2(cos2(c)+sin2(c))

As cos2(c)+sin2(c) = 1,

a2+b2 = R2

(a2+b2)1/2=R

So, overall:

acos(x)+bsin(x) = (a2+b2)1/2cos(x-arctan(b/a))

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3 years ago

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