Grade 12 Trigonometry Cde8F2

1. **Problem Statement:** Learn the basics of grade 12 trigonometry, including definitions, formulas, and applications. 2. **Key Concepts:** Trigonometry studies relationships between angles and sides in triangles, especially right triangles. 3. **Basic Functions:** The primary trigonometric functions are sine, cosine, and tangent, defined for an angle $\theta$ in a right triangle as: $$\sin \theta = \frac{\text{opposite}}{\text{hypotenuse}}, \quad \cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}}, \quad \tan \theta = \frac{\text{opposite}}{\text{adjacent}}$$ 4. **Important Identities:** - Pythagorean identity: $$\sin^2 \theta + \cos^2 \theta = 1$$ - Tangent identity: $$\tan \theta = \frac{\sin \theta}{\cos \theta}$$ 5. **Solving Triangles:** Given some sides or angles, use these functions and identities to find unknown values. 6. **Example:** If a right triangle has an angle $\theta = 30^\circ$ and hypotenuse $10$, find the opposite side. - Use $$\sin 30^\circ = \frac{\text{opposite}}{10}$$ - Since $$\sin 30^\circ = 0.5$$, then $$0.5 = \frac{\text{opposite}}{10}$$ - Multiply both sides by 10: $$\cancel{10} \times 0.5 = \cancel{10} \times \frac{\text{opposite}}{10} \Rightarrow 5 = \text{opposite}$$ 7. **Summary:** Trigonometry helps find unknown sides or angles using sine, cosine, tangent, and their identities. Practice by solving various triangle problems to master these concepts.