How do I solve this trig relationship???

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How do I solve this trig relationship???

Postby mb_atty on Thu Aug 11, 2011 1:02 pm

I have been given this by my teacher because i was complaining that the problems she gave in class were to easy:
B*tan(x) = C - D*cos(x)
B, C and D are known, I am trying to solve it to have a general expression for x. (0<x<pi/2)

This is driving me crazy!! I've admitted that I've been beat and have no idea how to solve it!! I've plotted it against x to check if there's a unique solution but I still have no idea how to solve it, help!!!!
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Re: How do I solve this trig relationship???

Postby nona.m.nona on Thu Aug 11, 2011 4:51 pm

mb_atty wrote:I have been given this by my teacher because i was complaining that the problems she gave in class were to easy:
B*tan(x) = C - D*cos(x)
B, C and D are known, I am trying to solve it to have a general expression for x. (0<x<pi/2)

One can fairly simply solve for the cosine in terms of the sine, but I'm not seeing anything obvious for solving for x in terms of only B, C, and D. It may be helpful that you're restricted to the first quadrant, so that each of sine and cosine are non-negative, but it may take a while to see quite how that might be helpful. If anything occurs to me, I'll post a follow-up.
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