SOLUTION: tan x + √3= 0 → tan x =−√3 The term tan x is now isolated in the equation. Find a particular solution on the interval (0, π). x =2π/3 , 0

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Question 786565: tan x + √3= 0 → tan x =−√3

The term tan x is now isolated in the equation. Find a particular solution on the interval (0, π).
x =2π/3 , 0 < x < π

On (-Infiniti, infiniti ), there are an infinite number of solutions. Write the general form of the solution. Your answer should be exact. (Use n as an integer constant. Enter your response in radians.)
x=???????????
Found 2 solutions by josmiceli, Edwin McCravy:
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
The tan is negative in the 2nd and 4th quadrants.
Between and radians, the solutions
are and
At both these angles,
-----------------------------------------
Now you have to go to
and then to
-------------------------------------
The progression is:




-------------
The general formula would be
( n = 0,1,2... )


Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
tan x + √3= 0 → tan x =−√3
The term tan x is now isolated in the equation. Find a particular solution on the interval (0, π).
x =2π/3 , 0 < x < π
On (-Infiniti, infiniti ), there are an infinite number of solutions. Write the general form of the solution. Your answer should be exact. (Use n as an integer constant. Enter your response in radians.)
x=???????????
Since tangent has period p, we can add any 
positive, negative, or zero multiple of p to 2p/3.

Answer = 2p/3 + np.

You could get an LCD of 3, and then factor out p on top and get , but that is not necessary.

Edwin
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