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Question
Find the principal solution and general solution of the following:
tan θ = `- 1/sqrt(3)`
Solution
The principal value of tan θ lies in `(- pi/2, pi/2)`
Since tan θ = `- 1/sqrt(3) > 0`
The principal value of tan θ lies in the IV quadrant.
tan θ = `- 1/sqrt(3)`
= `- tan pi/6`
tan θ = `tan ( - pi/6)`
θ = `- pi/6` is the principal solution.
The general solution of tan θ is
θ = `"n"pi - pi/6`, n ∈ Z
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