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Trigonometry solutions Question

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Summary: https://www.physicsforums.com/threads/trigonometry-question.977263/

Here's the question.
Find the solutions of the equation tan(x)=2cos(x)+1 if 0 ≤ x ≤ 2π.
I know this question can be solved by observing the graph but is there any other ways (like algorithms OR some Trigonometry rules) to solve this, I couldn't figure that out.
Thank you for those who noticed my question.

[Moderator's note: Moved from a technical forum and thus no template.]
 
Last edited by a moderator:

BvU

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Hello PhamCy, :welcome: !

Nice try, but PF asks a little more from you: make a start with the solution and we'll help you.

For example: substitute ##\tan x = {\sin x\over \cos x}## and see where it leads you
 
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see where it leads you
Way beyond what you can solve analytically with high school mathematics. WolframAlpha knows how to solve it analytically, here is one of the solutions:

equation.png
 

BvU

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Oops, I 'missed' the +1 which makes things difficult o:)
 

vela

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You could express the relationship as a polynomial in ##\cos\theta##, and then find the roots of the polynomial using something like Newton's method.
 

hunt_mat

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Turn everything into [itex]\cos x[/itex] to get:
[tex]
4\cos^{4}x+4\cos^{3}x+2\cos^{2}x-1=0
[/tex]
From here solve it using whatever method you like. I would advise you plotting the polynomial first.
 

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