



 
Abeth, If $\cos \theta = 1$ then $\sin \theta$ can't be $\frac12$ since you know that for any $\theta, \sin^2 \theta + \cos^2 \theta = 1.$ Hence is $\cos \theta = 1$ then $\sin \theta = 0.$ If $\cot \theta = \frac12$ then you know that $\large \frac{\cos \theta}{\sin \theta} = \frac12$ and hence \[\sin \theta = 2 \cos \theta.\] To find $\sin \theta \mbox{ and } \cos \theta$ square both sides of the equation above and use the fact that $ \sin^2 \theta + \cos^2 \theta = 1.$ Make sure you verify your answers. Penny  


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