# Roots on an equation

• September 27th 2010, 04:23 AM
Punch
Roots on an equation
The equation $2-cos^2\theta=Acos2\theta$ where $A$ is a constant, has a root $\theta=30^o$. Find all the other roots such that $\theta$ is between $0^o$ and $360^o$
• September 27th 2010, 06:10 AM
Quote:

Originally Posted by Punch
The equation $2-cos^2\theta=Acos2\theta$ where $A$ is a constant, has a root $\theta=30^o$. Find all the other roots such that $\theta$ is between $0^o$ and $360^o$

Did you manage to find A?
• September 27th 2010, 07:26 AM
Punch
Yes i did, A = 1.549
• September 28th 2010, 06:12 AM
Quote:

Originally Posted by Punch
Yes i did, A = 1.549

ok, then use the identity cos 2a = 2 cos^2 a -1
• September 30th 2010, 05:30 AM
Punch
Quote:

ok, then use the identity cos 2a = 2 cos^2 a -1

I guess the idea is to find the value of the constant A? How do I find the other roots after that? confused
• September 30th 2010, 06:32 AM
Quote:

Originally Posted by Punch
I guess the idea is to find the value of the constant A? How do I find the other roots after that? confused

2-cos^2 b = A cos 2b

2- cos^2 b = A (2cos ^2 b-1)

2- cos^2 b = 2A cos^2 b-A

Rearrange this: 2A cos^2 b+ cos^2 b- A- 2=0

(2A+1) cos^2 b - A -2 =0

Now you have got your A, plug it in here.
• September 30th 2010, 06:38 AM
Punch
Quote:

2-cos^2 b = A cos 2b

2- cos^2 b = A (2cos ^2 b-1)

2- cos^2 b = 2A cos^2 b-A

Rearrange this: 2A cos^2 b+ cos^2 b- A- 2=0

(2A+1) cos^2 b - A -2 =0

Now you have got your A, plug it in here.

sorry, but after substituting the value of A in, what do I do?
• September 30th 2010, 06:45 AM
$\cos b =\pm \sqrt{\frac{A+2}{2A+1}}$