1. **Problem Statement:** Create a mini-booklet learning guide summarizing Pre-Calculus key topics: the unit circle, six circular functions, graphs of these functions, and trigonometric identities. 2. **Unit Circle:** Draw a unit circle with angles labeled in degrees and radians, and mark coordinates $(\cos \theta, \sin \theta)$ for standard angles such as 0°, 30°, 45°, 60°, 90°, etc. 3. **Six Circular Functions:** Define\ - $\sin \theta = \frac{\text{opposite}}{\text{hypotenuse}}$\ - $\cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}}$\ - $\tan \theta = \frac{\sin \theta}{\cos \theta}$\ - $\csc \theta = \frac{1}{\sin \theta}$\ - $\sec \theta = \frac{1}{\cos \theta}$\ - $\cot \theta = \frac{1}{\tan \theta}$ Solve one problem per function, for example: Find $\sin 30^\circ$, which equals $\frac{1}{2}$. 4. **Graphs of Circular Functions:** Sketch or describe graphs of sine, cosine, and tangent over one period. - Sine graph starts at 0, peaks at 1 at $90^\circ$, returns to 0 at $180^\circ$. - Cosine graph starts at 1, drops to 0 at $90^\circ$, -1 at $180^\circ$. - Tangent graph has vertical asymptotes where cosine is 0, e.g., $90^\circ$. Include one observation per graph, e.g., "Sine wave oscillates between -1 and 1." 5. **Trigonometric Identities:** Include seven fundamental identities such as: $$\sin^2 \theta + \cos^2 \theta = 1$$ $$1 + \tan^2 \theta = \sec^2 \theta$$ Solve one example per identity, for instance verify at $\theta = 45^\circ$. 6. **Real-Life Connection:** Write a short paragraph explaining how trigonometry applies in fields such as engineering, navigation, or architecture. 7. **Creativity & Organization:** Use neat, colorful, and well-organized pages, either handmade or digital, folded A4 size. Final output is the compiled mini-booklet ready by October 17, 2025.