IGCSE/GCSE/O & A Level/IB/University Student Forum

Qualification => Subject Doubts => GCE AS & A2 Level => Math => Topic started by: ashwinkandel on September 27, 2011, 05:06:33 am

Title: Trigonometry Problem
Post by: ashwinkandel on September 27, 2011, 05:06:33 am: Hey guys, How to solve this : (http://i53.tinypic.com/2cpxj0h.png)
[Right Click the image and click view image to see the enlarged version]
Title: Re: Trigonometry Problem
Post by: astarmathsandphysics on September 27, 2011, 09:25:36 am: 5 mins
Title: Re: Trigonometry Problem
Post by: astarmathsandphysics on September 27, 2011, 09:32:38 am: Here
Title: Re: Trigonometry Problem
Post by: ashwinkandel on September 27, 2011, 03:26:15 pm: Thanks :)
Title: Re: Trigonometry Problem
Post by: astarmathsandphysics on September 27, 2011, 03:34:05 pm: There is a page for these problems on my website
All the C2 notes are here
http://astarmathsandphysics.com/a_level_maths_notes/a_level_maths_notes_c2_menu.html
Title: Re: Trigonometry Problem
Post by: angel_ak on November 13, 2011, 05:52:19 am: Express cos x + (under root 3) sin x in the form R cos ( x - a),
where R > 0 and 0 < a < 1/2 pie ,
giving the exact values of R and a.

m soryy i din knw how to insert that under root or pie symbol :(
reply sooon pleeeeeeeeeeease :(
Title: Re: Trigonometry Problem
Post by: angel_ak on November 13, 2011, 05:54:05 am: its from paper june 2007, p03 question 5
Title: Re: Trigonometry Problem
Post by: Arthur Bon Zavi on November 13, 2011, 07:25:05 am: Doing it.
Title: Re: Trigonometry Problem
Post by: Arthur Bon Zavi on November 13, 2011, 07:59:59 am: $cos x + \sqrt 3 sin x \equiv Rcos (x - a)$
= $cos x + \sqrt 3 sin x \equiv [(R) (cos x) (cos a)] + [(R) (sin x) (sin a)]$

Keeping x = 0, we get :
$1 \equiv R cos a$

Keeping x = $\frac{1}{2}\pi$ , we get :
$\sqrt3 \equiv R sin a$

R² = ( $\sqrt 3$ )² + (1)²
R = 2

There are two equations now :

$1 = 2cos a$ AND $\sqrt 3 = 2sin a$

Take any one of them and you will get the value of a, which is 60⁰ or $\frac {1}{3} \pi$ .

Therefore the equation is $cos x + \sqrt 3 sin x \equiv 2 cos (x - 60)$