Anja S.

Currently unavailable: until 10/09/2015

Degree: Mathematics (Masters) - Edinburgh University

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Hi!

My name is Anja and I am a currently in my third year of my Mmath (Masters of Mathematics) degree at the University of Edinburgh.

Previous Experience/Motivation

I have previously tutored at a local Kumon centre in my hometown for 3 years, where I helped children of all ages and capabilites in their Maths and English studies. The experience was rewarding and it showed me how students learn best: with Maths, understanding the key concepts rather than memorising formulae will serve you well, especially in passing exams with the higher grades! Another important point is build up the student's confidence so that they feel like they can attempt difficult problems and questions head on.

I understand that Maths can be confusing at times (I still get confused at times at university!) but it so satisfying when you get the 'aha!' moment and I hope I can be the person to give you your moments of sudden realisation.

The Sessions

My aims in the sessions would be to establish the student's current knowledge and fill in any gaps or clarify points. Then improve their understanding by attempting various problems. Finally, it is important for the student to try and explain what they have learnt in the session as this will show what they have understood. Explaining a mathematical concept to another person will show true understanding and will aid in the student's revision much more than memorising formulae.

If you have an further questions send me a 'WebMail' or book a 'Meet the Tutor Session'.

I look forward to hearing from you all!

#### Subjects offered

SubjectLevelMy prices
Maths A Level £20 /hr
Maths GCSE £18 /hr

#### Qualifications

MathematicsA-LevelA*
PhysicsA-LevelA
Further MathematicsA-LevelB
 CRB/DBS Standard No CRB/DBS Enhanced No

### Show that the integral of tan(x) is ln|sec(x)| + C where C is a constant.

First, recall that tan(x) can be rewritten in terms of sine and cosine. tan(x) = sin(x)/cos(x) The rephrasing of our question suggests that we should try the substitution rule of integration. We should substitute u=cos(x), since then du = -sin(x) dx and so sin(x) dx = -du So the integral of...

First, recall that tan(x) can be rewritten in terms of sine and cosine.

tan(x) = sin(x)/cos(x)

The rephrasing of our question suggests that we should try the substitution rule of integration.

We should substitute u=cos(x), since then du = -sin(x) dx and so sin(x) dx = -du

So the integral of tan(x) = the integral of sin(x)/cos(x) = the integral of -1/u = - ln|u| +C = - ln|cosx| +C

Now, - ln|cos(x)| = ln(|cos(x)|-1) = ln(1/|cos(x)|) = ln|sec(x)|

Therefore, the integral of tan(x) is ln|sec(x)| + C

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2 years ago

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