## hl trigonometric equations

Discussions for the Core part of the syllabus. Algebra, Functions and equations, Circular functions and trigonometry, Vectors, Statistics and probability, Calculus. IB Maths HL Revision Notes

### hl trigonometric equations

2sin(x+(π)/(3))+2sin(x-(π)/(3))=√(3)

ib231997

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Joined: Wed Apr 24, 2013 12:17 pm

### Re: hl trigonometric equations

ib231997 wrote:2sin(x+(π)/(3))+2sin(x-(π)/(3))=√(3)

You have to use the following trigonometric identities:

$sin(A+B)=sinAcosB+cosAsinB$

and

$sin(A-B)=sinAcosB-cosAsinB$

So

$sin(x+\frac{\pi}{3})=sinxcos(\frac{\pi}{3})+cosxsin(\frac{\pi}{3})$ where k takes integer values.

and

$sin(x-\frac{\pi}{3})=sinxcos(\frac{\pi}{3})-cosxsin(\frac{\pi}{3})$

Therefore, your equation now looks like this

$sinxcos(\frac{\pi}{3})+cosxsin(\frac{\pi}{3})+sinxcos(\frac{\pi}{3})-cosxsin(\frac{\pi}{3})=\frac{\sqrt 3}{2}$

$2sinxcos(\frac{\pi}{3})=\frac{\sqrt 3}{2}$

$2sinx \frac{1}{2}=\frac{\sqrt 3}{2}$

$sinx=\frac{\sqrt 3}{2}$

$x=2k\pi +\frac{\pi}{3}$ or $x=2k\pi +\pi -\frac{\pi}{3}$

Hope these help!!
miranda

Posts: 268
Joined: Mon Jan 28, 2013 8:03 pm