We want to find the six trig functions of the angle given in terms of that of its reference angle.
[tex]\theta=\frac{7\pi}{9}[/tex]
This is a sketch of the angle;
This is smaller that 360, so it cant be reduced further, It is the reference angle.
So;
[tex]\begin{gathered} \sin \theta=\sin \frac{7\pi}{9} \\ \cos \theta=\cos \frac{7\pi}{9} \\ \tan \theta=\frac{\sin \frac{7\pi}{9}}{\cos \frac{7\pi}{9}} \\ \csc \theta=\frac{1}{\sin \frac{7\pi}{9}} \\ \sec \theta=\frac{1}{\cos \frac{7\pi}{9}} \\ \cot \theta=\frac{1}{\tan\theta}=\frac{\cos \frac{7\pi}{9}}{\sin \frac{7\pi}{9}} \end{gathered}[/tex]
These are our trigonometric ratios.
