Use the Half-angle Formulas to find the exact value of the trigonometric function.
-$\cos 22.5 ^ { \circ }$
A) $\frac { 1 } { 2 } \sqrt { 2 - \sqrt { 2 } }$
B) $- \frac { 1 } { 2 } \sqrt { 2 - \sqrt { 2 } }$
C) $- \frac { 1 } { 2 } \sqrt { 2 + \sqrt { 2 } }$
D) $\frac { 1 } { 2 } \sqrt { 2 + \sqrt { 2 } }$

Question

Quizplus · Accepted Answer

The half-angle formula for cosine is $\cos \frac{\theta}{2} = \pm \sqrt{\frac{1 + \cos \theta}{2}}$. For $\theta = 45^\circ$, $\cos 45^\circ = \frac{\sqrt{2}}{2}$, so $\cos 22.5^\circ = \sqrt{\frac{1 + \frac{\sqrt{2}}{2}}{2}} = \frac{1}{2}\sqrt{2 + \sqrt{2}}$.

Use the Half-Angle Formulas to Find the Exact Value of the Trigonometric