find sin theta

From the Pythagorean identity,

sin² θ  +  cos² θ     =  1        Plug in  -10/11  for  cos θ .

sin² θ  +  (-10/11)²  =  1       \((-\frac{10}{11})^2=(-\frac{10}{11})(-\frac{10}{11})=\frac{100}{121}\)

sin² θ  +  100/121   =  1       Subtract   100 / 121  from both sides.

sin² θ   =   21/121                Since sin is negative in Quad III, take the negative sqrt of both sides.

sin θ     =  \(-\sqrt{\frac{21}{121}}\)

sin θ     =   \(-\frac{\sqrt{21}}{11}\)