My Math Forum How can I find the angle X

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 February 8th, 2013, 07:25 PM #1 Newbie   Joined: Feb 2013 Posts: 5 Thanks: 0 How can I find the angle X [a*cos(b-X)]^2 = c*cos(X) where a, b, c are constant
 February 8th, 2013, 10:19 PM #2 Senior Member   Joined: Dec 2012 Posts: 148 Thanks: 0 Re: How can I find the angle X I am not sure about this problem... Could you check if you posted it right?!
 February 9th, 2013, 01:25 AM #3 Newbie   Joined: Feb 2013 Posts: 5 Thanks: 0 Re: How can I find the angle X HI Yes it is OK. There is one unknown and one equation and I am stuck in solving the angle X.
 February 9th, 2013, 01:46 AM #4 Newbie   Joined: Feb 2013 Posts: 5 Thanks: 0 Re: How can I find the angle X Or alternatively I want to find the solution of equation given below [a*cos(x)]^2 + b*sin(x)*cos(x) + c = cos(x) where a, b and c are constant Thanks.
 February 9th, 2013, 10:22 PM #5 Senior Member   Joined: Dec 2012 Posts: 148 Thanks: 0 Re: How can I find the angle X $[a \cdot \cos (b-x)]^2= c \cdot \cos x \; \text{where a, b, c are constant}$ Put random numbers for a, b, c (radians), try to solve and then generalize for a, b, c.
February 9th, 2013, 10:35 PM   #6
Math Team

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Re: How can I find the angle X

Quote:
 Originally Posted by Yasir [a*cos(b-X)]^2 = c*cos(X) where a, b, c are constant
Hint : Expand cos(b-x) and try writing the whole equation in terms of cos(x). It will result a quartic equation. Solving it and handling the periods would be sufficient for finding 'x'.

Quote:
 Originally Posted by tahir.iman Put random numbers for a, b, c (radians), try to solve and then generalize for a, b, c.
Wha? Why would one do that??

 February 9th, 2013, 11:50 PM #7 Newbie   Joined: Feb 2013 Posts: 5 Thanks: 0 Re: How can I find the angle X Thanks a lot for your help. I am trying to solve this its not as simple as it looks like e.g. i am not able to find quadratic equation with only cos(x) term.
February 10th, 2013, 01:10 AM   #8
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Re: How can I find the angle X

Quote:
 Originally Posted by Yasir i am not able to find quadratic equation
I didn't said quadratic, did I? I said 'quartic'. A polynomial of degree 4.

 February 10th, 2013, 03:07 AM #9 Newbie   Joined: Feb 2013 Posts: 5 Thanks: 0 Re: How can I find the angle X Thanks for the clarification. I will try again to write whole equation in terms of cos(x). Previously I was ended up with an equation having one extra sin(x) term. I will try again to get rid of sin(x). Thanks.
 February 10th, 2013, 03:16 AM #10 Math Team     Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory Re: How can I find the angle X Try the Pythagoras theorem for writing out sin(x) in terms of cos(x), the whole calculation can get a bit messy . . .

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