trigonometry

A-Maths: Full Derivation of R-formula

Last week, I taught my class on the topic of R-formula in A-Maths Trigonometry.

I highlighted that schools taught the usage of the two formulas as shown:

In my years of teaching, I have also come across schools which have insisted students to understand and use the full derivation of R-formula to solve the questions. Last night, my student who was sure that her school did not teach full derivation contacted me to help her as she was told at the very last minute that full derivation of R-formula will be tested in her test.

I have included the step-by-step working here. It includes the usage of addition formula and identity formula.

For those who prefer to hear from my explanation, I have included the video (duration: 6 minutes).

I would love to hear from you if you understand how R-formula is derived. Leave me your comment below.

E-Maths Trigonometry Workshop Post Mortem

I completed my E-Maths Trigonometry workshop with a group of sportsmen and sportswomen. We do running, archery, basketball, badminton, bowling...

It was exciting and nervous to meet new faces... They hear my stories, I hear theirs.

For the workshop, I would like to discuss about bearings and the usage of sin formula through this question. Do you have any difficulties in E-Maths Trigonometry? I would love to hear from you! Leave your thoughts in the comment section below.

Trigonometry E-Maths Question

For bearings, pay attention to these 3 points:

3 figures
Reference point
Measured from North in a clockwise direction

For sin formula, you must know how to identify an angle and its corresponding length which are opposite each other.

View the video via this link: http://www.youtube.com/watch?v=JhH1zqwn9uM

25% of 2010 'O' Level E-Maths Paper 2 is on Trigonometry

I was looking at this year 'O' Level E-Maths Papers. They were overall 'friendly' with hardly any surprise. I shall not term the papers as easy or hard.

I was paying attention to the concepts on Trigonometry and it's interesting to note that the typical short question didn't appear in Paper 1 instead there were 2.5 questions linked very closely to Trigonometry.

Why Trigonometry you might ask?

Well, many students might not be aware Trigonometry is a fundamental set of formulas and concepts which are closely linked to arc lengths, area of sector, mensuration and any questions involving angles in triangle, area of triangles...

I can't show you the questions due to copyright but you can get a copy of Ten Years Series book (released in January 2011).

Questions on Trigonometry in 2010 'O' Level E-Maths Paper 2

Question 1 (10 marks) tests candidates on

TOA CAH SOH (extensively since the diagram consists of 3 right angle triangles). I suspect some might use SIN rule (nothing wrong but more manipulations) instead of TOA CAH SOH to answer the questions
Understanding of bearings

Question 7 (11 marks) tests candidates on

Usage of COS rule to find angle
Ability to 'see' and find angle of depression from paper
Manipulation of area of triangle using formula with 'sin'

Question 8bii (4 marks) tests candidates on

Ability to find the height of a triangular surface using TOA CAH SOH

The challenges many students face include:

Knowing all the formulas but not being able to select the correct approach fast and accurate enough in test and exams.
Not being able to 'see' 3D from paper.
Lacking the flexibility to manipulate formulas (due to poor Algebraic foundation in Secondary 1 and 2)
Not learning from repeated mistakes
Unaware of the misconceptions
Assumption that you know the important usage of every formula but in fact you don't

If your child is not scoring 'A' for E-Maths, he must know the reason and be prepared to do something about it. In 'O' Levels, A1 is unlikely to be 75% and above. It is determined by the bell curve of the entire cohort.

Trigonometry is a very important section in E-Maths and A-Maths. I would like to share with your child the strategies proven to have helped my students to achieve better results in their exams.

Join me in the Dec Trigonometry Workshop today! Click here to read more.

A-Math: How to Integrate Trigonometry with Square Power [video]

Some students get really confused between differentiation and integration of Trigonometry. In fact, I personally feel that integration of Trigonometry is easier as there are only 3 general formulas (as shown). In this video, I've shown the thinking process, step by step approach on how to integrate Trigonometry with square power, an advanced concept. Hope you find the approach and explanation useful.

I would love to hear your comments.

Click on this link to view the video: http://www.youtube.com/watch?v=E3ykmKa4MLU

O Level A-Math Trigonometry Basics : How Do We Know Which Formula To Use?

For the past month, other than being busy with the June Intensive Revision Programmes, I was also packed with Mid Year Exam Papers Review for my group of students.

I am pleased to announce that almost all see an improvement in their Mid Year Results (One boy has his grades jump from F9 to A2! Congrats, B!)

I was reviewing the school a-Math exam papers with one of my students during my A-Math Ultimate Leap Programme when she posted me a good question.

Let's take a look at her Trigonometry question first:

This was her solution for the question:

There is one misconception in her thoughts, can you spot it?

sin 3x is not equal to sin x + sin 2x!

In fact, the correct formula to choose for this question is

sin 3x = sin (2x + x)

= sin2xcosx + cos2xsinx

Her question was: how do you know which formula to use?

TIP: When the angle involved is ODD, we usually use addition formula (just like in this question).

When angle is EVEN, double angle formula is perhaps the correct one to choose.

Are you confused just like my student, which formula should be use? Leave me a comment.

I hope this post has made your understanding clearer :-)

Below is a list of useful posts on A-Math Trigonometry:

PS: I will be re-running A-Math Trigonometry Mastery Workshop in July as some students miss out the one in June due to other commitments. Registration is open! Click here for more details

'O' Level A-Math Essential Concepts Revision Workshop

For more details, click here