If $\tan \theta = - \frac{1}{{\sqrt 3 }}$ and $\sin \theta = \frac{1}{2}$, $\cos \theta = - \frac{{\sqrt 3 }}{2}$, then the principal value of $\theta $ will be
$\frac{\pi }{6}$
$\frac{{5\pi }}{6}$
$\frac{{7\pi }}{6}$
$ - \frac{\pi }{6}$
The solution set of the system of equation
$x\,\, + \,\,y\,\, = \,\,\frac{{2\pi }}{3},\,{\rm{cos}}\,{\rm{x + }}\,{\rm{ cos}}\,{\rm{y}}\,{\rm{ = }}\,\frac{3}{2},$ where $x$ and $y$ are real in
The most general value of $\theta $ satisfying the equations $\sin \theta = \sin \alpha $ and $\cos \theta = \cos \alpha $ is
The number of solutions of the equation $\sin x=$ $\cos ^{2} x$ in the interval $(0,10)$ is
If $\sin {\rm{ }}\left( {\frac{\pi }{4}\cot \theta } \right) = \cos {\rm{ }}\left( {\frac{\pi }{4}\tan \theta } \right)\,\,,$ then $\theta = $
If both roots of quadratic equation ${x^2} + \left( {\sin \,\theta + \cos \,\theta } \right)x + \frac{3}{8} = 0$ are positive and distinct then complete set of values of $\theta $ in $\left[ {0,2\pi } \right]$ is