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Solve the equation for x in the interval [0,2π). Use exact solutions where possible and give approximate solutions correct to four decimal places.

Solve the equation for x in the interval [0,2π). Use exact solutions where possible-example-1

1 Answer

6 votes

From the problem, we have an equation of :


2\tan ^2x+3\tan x+1=0

Factor completely :


(2\tan x+1)(\tan x+1)=0

Equate both factors to 0 :


\begin{gathered} 2\tan x+1=0 \\ 2\tan x=-1 \\ \tan x=-(1)/(2) \\ x=\arctan (-(1)/(2)) \\ x=-26.565\ldots \end{gathered}
\begin{gathered} \tan x+1=0 \\ \tan x=-1 \\ x=\arctan (-1) \\ x=(1)/(4)\pi,(3)/(4)\pi \end{gathered}

The only exact values of x are π/4 and 3π/4

The answers are π/4 and 3π/4

User HobbitOfShire
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