singaporeolevelmathstrigo proving | singaporeolevelmaths http://www.singaporeolevelmaths.com Simple Tips for Better Maths Results! Thu, 05 Jan 2012 14:02:12 +0000 en hourly 1 http://wordpress.org/?v=3.0.4 O Level Additional Math – How To Prove Trigonometry Identity http://www.singaporeolevelmaths.com/2008/09/29/o-level-additional-math-how-to-prove-trigonometry-identity/ http://www.singaporeolevelmaths.com/2008/09/29/o-level-additional-math-how-to-prove-trigonometry-identity/#comments Mon, 29 Sep 2008 05:34:11 +0000 Ai Ling http://singaporeolevelmaths.com/?p=316
Dear Ms Ong,
i had just taken my class test on simple trigonometric identities and well as further trignonometric identities yesterday.
sadly to say, i left all the proving of trigonometric identities blank which is worth a total of 9 marks.
Im starting to get panic about trigonometric identities for my coming common test,end of year exams as well as the big O Level.
so im actually here to ask you if you may guide me on how to do them in a faster way, because i realised ive no time to tackle those proving questions.
Best Wishes,
Priscilla Fong

I received this email among the many others in my mailbox. I think this is a common problem face in proving Trigo Identity question. I shall provide a few strategies to handle this sort of question.

  • Usually start with the left hand side or whichever side which is more complicated.
  • When given trigo functions in the form of sec, cosec or cot x , it is advisable to change it to basic trigo functions like sin, cos, tan
  • When question involves power (especially square power), formulas should be considered.
  • Have the END in mind before you begin i.e if the end result involves only sin, your working should eventually eliminate the other trigo functions and stick on to sin.
  • It should take less than 8 steps for a 3-4 marks proving question.
  • a^2-b^2=(a+b)(a-b) is sometimes used in proving Trigo Identity. (Algebra rule)

I am going to use an example to illustrate how to use the above strategies

Q: Prove the identity (sec A - tan A)^2 = {1- sin A}/{1+ sin A}

(sec A - tan A)^2 =( {1}/{ cos A}-{sin A}/{cos A})^2 (Change sec and tan into sin & cos)

=  ( {1 - sin A}/{cos A})^2

= {(1-sin A)^2}/{(cos A)^2} 

=  {(1 - sin A)(1 - sin A)}/{(1 - sin^2 A)} (applying formula)

= {(1 - sin A)(1 - sin A)}/{(1 - sin A)(1 + sin A)}  (applying algebraic rule)

= {1 - sin A}/{1 + sin A}  (Proven)

Total number of steps = 6

Additional resource: You may want to read on A-Math Trigo Graphs here.

]]> http://www.singaporeolevelmaths.com/2008/09/29/o-level-additional-math-how-to-prove-trigonometry-identity/feed/ 5 A-Math Trigo Qn http://www.singaporeolevelmaths.com/2007/09/26/a-math-trigo-qn/ http://www.singaporeolevelmaths.com/2007/09/26/a-math-trigo-qn/#comments Wed, 26 Sep 2007 02:10:00 +0000 Ai Ling http://singaporeolevelmaths.com/2007/09/26/a-math-trigo-qn/ Another question from O Level Additional Mathematics (A-Math).

If p =( 1 + cosx )/sinx, 1/p= ( 1 – cosx )/( sinx ), find sinx and cosx in terms of p.

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