Blog: Find the principal solutions of the equation tan x = -1/√3

Thursday, May 12, 2011

Find the principal solutions of the equation tan x = -1/√3

$\displaystyle{\tan{{x}}}=-\frac{{1}}{\sqrt{{3}}}$

Isolate angle x.

$\displaystyle{x}={{\tan}}^{{-{1}}}{\left(-\frac{{1}}{\sqrt{{3}}}\right)}$

Using a calculator to compute, it yields a value:

$\displaystyle{x}=-{{30}}^{{o}}$

Since it states to find the principal solution of the given equation, it restricts the values of the angle from $\displaystyle{{0}}^{{o}}$ to $\displaystyle{{360}}^{{o}}$ . To determine the values of x in this interval, take note that tangent has negative values in Quadrants II and IV.