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

Algebra ->  Trigonometry-basics -> 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       Log On


   



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) About Me  (Show Source):
You can put this solution on YOUR website!
The tan is negative in the 2nd and 4th quadrants.
Between +0+ and +2%2Api+ radians, the solutions
are +x+=+%282%2Api%29%2F3+ and +x+=+%28+5%2Api%29%2F3+
At both these angles, +tan%28x%29+=+-sqrt%283%29+%2F+1+
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Now you have to go to +2%2Api+%2B+%282%2Api%29%2F3+=+%288%2Api%29%2F3+
and then to +2%2Api+%2B+%285%2Api%29%2F3++=+11%2Api%2F3+
-------------------------------------
The progression is:
+%282%2Api%29%2F3+
+%285%2Api%29%2F3+
+%288%2Api%29%2F3+
+%2811%2Api%29%2F3+
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The general formula would be
+x+=+%28%28+2+%2B+3n+%29%2Api%29+%2F+3+ ( n = 0,1,2... )


Answer by Edwin McCravy(20054) About Me  (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 %282%2B3n%29pi%2F3, but that is not necessary.

Edwin