"HALF OF YOU" Description: In this activity the students will be able to si rigonometric expressions applying half-angle identities Directions: Simplify the following trigonometric expressions using angle identities. \( \begin{array}{ll}\text { 1. } \frac{1-\cos 13^{\circ}}{\sin 18^{\circ}} & \text { 6. }-\frac{1-\cos 270^{\circ}}{\operatorname{tin} 270^{\circ}} \\ \text { 2. } \sqrt{\frac{1-\cos 43^{\circ}}{2}} & \text { 7. }-\sqrt{\frac{1-\cos 200^{\circ}}{1+\cos 200^{\circ}}} \\ \text { 3. }-\frac{\sin 276^{\circ}}{1+\cos 276^{\circ}} & \text { 8. } \sqrt{\frac{1-\cos 39^{\circ}}{1+\cos 39^{\circ}}} \\ \text { 4. } \sqrt{\frac{1-\cos 82^{\circ}}{2}} & \text { 9. } \sqrt{\frac{1+\cos 25^{\circ}}{2}} \\ \text { 5. } \frac{\sin 99^{\circ}}{1+\cos 96^{\circ}} & \text { 10. }-\sqrt{\frac{1+\cos 212^{0}}{2}}\end{array} \)

Did you know that half-angle identities come from applying the sine and cosine formulas to angles that are halved? This nifty algebraic magic helps in simplifying trigonometric expressions by relating them back to more familiar angles, making solving problems much more straightforward. For instance, if you break down an angle like \(45^\circ\) into \(22.5^\circ\), you’ll find it’s a breeze to calculate sine and cosine with the half-angle formulas! In a real-world application, half-angle identities are incredibly useful, especially in fields like engineering and physics. When analyzing wave patterns or sound frequencies, understanding these identities can simplify complex equations, allowing professionals to model real-world phenomena more accurately. So next time you admire a bridge or enjoy music, remember that half-angle identities might just be working behind the scenes!