## Precalculus (6th Edition) Blitzer

We know that this statement does not make sense because to calculate the value of $\cos 100{}^\circ$ using the half angle formula, it is required to know the value of $\cos 200{}^\circ$. \begin{align} & \cos \frac{\alpha }{2}=\pm \sqrt{\frac{1+\cos \alpha }{2}} \\ & \cos \frac{200{}^\circ }{2}=\pm \sqrt{\frac{1+\cos 200{}^\circ }{2}} \\ & \cos 100{}^\circ =\pm \sqrt{\frac{1+\cos 200{}^\circ }{2}} \end{align} Clearly, the value of $\cos 200{}^\circ$ can be computed with the help of the calculator but there is no known trigonometric value of $200{}^\circ$ angle.