Trigo (A maths)

• anpanman

  21 Sep 09, 22:03

  Without using a calculator, evaluate the value of

  sin [2 sin-1 (0.6)]

  cos[sin-1(-4/5) + tan-1 (4/7)]

  They are some inverse trigo functions and are questions found from the TYS. Don't recall my teacher having taught us how to find the value from inverse functions? Is it out of our syllabus? Whatever the case , please teach me how to solve the following questions. Thank you!

• wee_ws

  21 Sep 09, 22:25

  Hi,

    Let x = arcsin (0.6).

    We want to find the value of sin 2x, which is 2 sin x cos x.

    Now sin x = 0.6, by definition. With this result, draw a right-angled triangle to find cos x, which is 0.8 or 4/5.

    As for your second question, let x = arcsin (-4/5) and y = arctan (4/7).

    We want to find the value of cos (x + y), which is cos x cos y - sin x sin y.

    Again, draw right-angled triangles to find the necessary values of trigo ratios in the expression of cos (x + y).

    Thanks!

  Cheers,
  Wen Shih

     

• Mikethm

  22 Sep 09, 02:09

  Originally posted by anpanman:

  Without using a calculator, evaluate the value of

  sin [2 sin-1 (0.6)]

  cos[sin-1(-4/5) + tan-1 (4/7)]

  They are some inverse trigo functions and are questions found from the TYS. Don't recall my teacher having taught us how to find the value from inverse functions? Is it out of our syllabus? Whatever the case , please teach me how to solve the following questions. Thank you!

  It is in the syllabus. In fact, this is the 1st time principal values of trigo ratios is in O/N syllabus. However it is ok not to know it as I am not aware of any schools that teach it. Everyone wrong together loh. kekeke

  For the 1st question, draw a triangle in the 1st quadrant.

  For the 2nd one, the triangles are in the 4th quadrant (arcsin -ve) and in the 1st quadrant (for arctan +ve).

  Question on principal values had been asked in the 2008 GCE N level I believe.

• Lee012lee

  22 Sep 09, 02:51

  Originally posted by anpanman:

  Without using a calculator, evaluate the value of

  sin [2 sin-1 (0.6)]

  cos[sin-1(-4/5) + tan-1 (4/7)]

  They are some inverse trigo functions and are questions found from the TYS. Don't recall my teacher having taught us how to find the value from inverse functions? Is it out of our syllabus? Whatever the case , please teach me how to solve the following questions. Thank you!

  These 2 questions are printed in the 2008 Shing Lee Add. Maths TYS.

  It is to be noted that these two questions are provided by the publisher Shing Lee and these two questions are not the actual past year "O" level add maths questions.

  Inverse trigonometric functions are not in the new syllabus of "O" level Add Maths.

  Inverse trignometric functions are only tested in H1 Maths syllabus.

  Hua Yi Secondary School, Swiss Cottage, Clementi Town Secondary School and some other school teachers have taught their students the ways to solve these questions as these questions are printed in the 2008 Shing Lee Add Maths TYS but the teachers have also told their students that inverse trigonometric functions are not in their syllabus. But the teachers told the students that these questions are good for the better understanding of the concepts.

  PS : 2008 "N" level Maths merely tested the the obtuse angles for TOA, CAH and SOH. Obtuse angles for TOA CAH SOH have been tested in "O" level EMaths for many years now and it is the first time that obtuse angles for TOA CAH SOH have been tested in 2008 "N" level Maths. It is not about the principal values of inverse trigonometric functions.

   

• wee_ws

  22 Sep 09, 08:11

  Hi,

    Many H2 Maths students struggle with inverse trigo concepts too.

    Just during my last lesson, two students from IP programme clarified with me on inverse trigo. They asked if 1/(tan x) was equal to arctan x. It is a common to see students get mixed up with the ideas of reciprocal and inverse.

    When we say reciprocal of tan x, we mean 1/(tan x).

    When we refer to arctan x,  we mean: 

    k = arctan x <=> tan k = x.

    Thanks!

  Cheers,
  Wen Shih

• Mikethm

  22 Sep 09, 16:27

  Originally posted by Lee012lee:

  These 2 questions are printed in the 2008 Shing Lee Add. Maths TYS.

  It is to be noted that these two questions are provided by the publisher Shing Lee and these two questions are not the actual past year "O" level add maths questions.

  Inverse trigonometric functions are not in the new syllabus of "O" level Add Maths.

  Inverse trignometric functions are only tested in H1 Maths syllabus.

  Hua Yi Secondary School, Swiss Cottage, Clementi Town Secondary School and some other school teachers have taught their students the ways to solve these questions as these questions are printed in the 2008 Shing Lee Add Maths TYS but the teachers have also told their students that inverse trigonometric functions are not in their syllabus. But the teachers told the students that these questions are good for the better understanding of the concepts.

  PS : 2008 "N" level Maths merely tested the the obtuse angles for TOA, CAH and SOH. Obtuse angles for TOA CAH SOH have been tested in "O" level EMaths for many years now and it is the first time that obtuse angles for TOA CAH SOH have been tested in 2008 "N" level Maths. It is not about the principal values of inverse trigonometric functions.

   

  Please refer to the following syllabus outlines extracted from SEAB website.

  

  

   

  And if my lone N level Additional Mathematics student was not smoked by her teacher, these are the actual N level 2008 AM questions... refer to question 2.

  

• Lee012lee

  22 Sep 09, 17:02

  Hi Mikethm,

  Thanks for the information.

  I stand to be corrected for my mistakes and misinformation from other sources.

  Please accept my apologies.

  Regards.

• Mikethm

  22 Sep 09, 18:24

  Originally posted by Lee012lee:

  Hi Mikethm,

  Thanks for the information.

  I stand to be corrected for my mistakes and misinformation from other sources.

  Please accept my apologies.

  Regards.

  1st there is no apologies required. This is just a discussion not a debate/argument.

  2nd, I still might be wrong about those questions being the actual N level AM questions as it did not come 1st hand to me. Perhaps someone here can verify if those are the 2008 N level questions.

  Perhaps wee_ws could monopolise the N(Academic) Additional Mathematics TYS market by publishing it... the NA AM TYS is not available on the market at all despite there being a sizable target audience.

• wee_ws

  22 Sep 09, 18:39

  Hi Mikethm and Lee012lee,

    Thanks, I wish to counter-offer :P

    Would you like to consider helping Dyna on the N(A) Add Maths TYS?

    I could help you liaise with the boss, if you are keen :)

    Thanks!

  P.S. I just dropped an email to Dyna to enquire if it is interested to publish this TYS.

  Cheers,
  Wen Shih

• SBS n SMRT

  22 Sep 09, 21:23

  Do not buy SHing lee ones, they like to add in some jialat qns.......not o level.....use dyna or sap

• Mikethm

  22 Sep 09, 23:27

  Originally posted by wee_ws:

  Hi Mikethm and Lee012lee,

    Thanks, I wish to counter-offer :P

    Would you like to consider helping Dyna on the N(A) Add Maths TYS?

    I could help you liaise with the boss, if you are keen :)

    Thanks!

  P.S. I just dropped an email to Dyna to enquire if it is interested to publish this TYS.

  Cheers,
  Wen Shih

  Would be great if Lee would take up the offer.

• Mikethm

  22 Sep 09, 23:50

  Originally posted by SBS n SMRT:

  Do not buy SHing lee ones, they like to add in some jialat qns.......not o level.....use dyna or sap

  Yes, the ShingLee TYS got some jialat questions but only when there were no existing past year questions. The geometry proof unit was especially badly done. The EM one for this year was bad because they spread the 2008 questions into the topics instead of having it as a paper at the end.

  However, it is the best organised among the various TYS with year by year questions not omitted where they exist. For the E Maths one, the summary points is especially useful because I can't be bothered going thru 4 years' of textbooks. In fact, I asked my lone sec 1 student to buy a copy so that she does not have to hunt thru the textbook for a concept.

  Every year, I buy one copy of the SAP, Dyna and ShingLee TYS to compare. And almost every year, my choice have been the ShingLee Pass with Distinction as the main material with the Dyna Year by Year format TYS for the final revision which I prefer to be done in a paper format.

  If I were to live with only 1 TYS, I would buy the ShingLee one...

• Lee012lee

  23 Sep 09, 12:47

  Originally posted by Mikethm:

  Would be great if Lee would take up the offer.

  I have TYS under my name before in the past.

  But the pay is very little as compared to teaching or tutoring.

  The market for "N" level Add Maths is too small and the minimum print for each

  TYS is about 1000 - 2000 copies. So, Dyna might not be interested.

  Hi Mikethm, Dyna provides the service of compiling of actual past year exam

  papers for less popular subjects at a low fee ie Dyna will compile the actual "N"

  level Add Maths questions into a booklet and sells it for a few dollars.

  Dyna had helped me to compile the "AO" level Maths questions into a booklet in

  the past for my "AO" Maths students.

• absol

  23 Sep 09, 13:18

  OT a bit, my sch bkshop says dyna dont want to print a level physics H2 year by year paper this yr, anywhere i can find TYS from other publishers printing year by year(if there are)?

  its kinda useless to practice topic by topic for a level exam....

• Lee012lee

  23 Sep 09, 13:58

  You can approach Dyna to ask for the compilation of the H2 physics examination questions year by year. 

  You will need to go to its premises to request for the compilation.

  Dyna is located in Henderson Industrial Park, near Bukit Merah Central.

   

• Lee012lee

  23 Sep 09, 23:40

  Originally posted by wee_ws:

  Hi Mikethm and Lee012lee,

    Thanks, I wish to counter-offer :P

    Would you like to consider helping Dyna on the N(A) Add Maths TYS?

    I could help you liaise with the boss, if you are keen :)

    Thanks!

  P.S. I just dropped an email to Dyna to enquire if it is interested to publish this TYS.

  Cheers,
  Wen Shih

  Hi Mr Wee,

  I have sent you a private message.

  Thanks.

  Regards.

• Chatter freako

  1 Oct 09, 21:44

  Those are the N level 08 papers. Whats wrong with those questions? My teacher says its principal value. Nothing much actually... Just use your calculator rite? And at most its in pie.

• qdtimes2

  1 Oct 09, 22:16

  Originally posted by Chatter freako:

  Those are the N level 08 papers. Whats wrong with those questions? My teacher says its principal value. Nothing much actually... Just use your calculator rite? And at most its in pie.

  we need to show the workings on how we do it without using the calculator, as it's asked by the qn but sometimes, we can use calculator to check our answers.

• Redgreenapples

  1 Oct 09, 23:23

  hi, i'm currently searching for nlevel amath tys or sch papers but couldn't find them. T_T

  am taking the subj as a private candidate so hope to have them.

  any kind soul who can send them to me??thanks.

• wee_ws

  1 Oct 09, 23:37

  Hi,

    Please check your mailbox. Btw, you are doing sec 4N as private candidate?

    Thanks and good luck!

  Cheers,
  Wen Shih

• Redgreenapples

  3 Oct 09, 14:35

  yea, this year trying to do sec4N as private.

  hope can pass! then maybe next year try out for o level. :D
  thank you so much.