# Trigonometry solutions Question

#### PhamCy

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.

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#### BvU

Homework Helper
Hello PhamCy, !

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

• Greg Bernhardt

#### mfb

Mentor
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: #### BvU

Homework Helper
Oops, I 'missed' the +1 which makes things difficult • Delta2 and Klystron

#### vela

Staff Emeritus
Homework Helper
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.

• Delta2

#### hunt_mat

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

• Delta2

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